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Palindromic Decremented Squares
of the form n^2–x
rood n(n+0) rood n(n+1) rood n(n+2) rood n(n+x) rood
rood n^2+1 rood n^2+x rood
rood n^2+(n+1) rood n^2+(n+x)



Introduction

Palindromic numbers are numbers which read the same from
 p_right left to right (forwards) as from the right to left (backwards) p_left
Here are a few random examples : 7, 3113, 44611644

Decremented Square numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
So, this line is for experts only

base2 – X


Palindromic Decremented Squares

Decremented Squares of the form x2 – 0 can only start or end with a 0, 1, 4, 5, 6 or 9
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by 2 : 52
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
9 can only be followed by an even number : 90, 92, 94, 96 or 98

Decremented Squares of the form x2 – 1 can only start or end in one of the following digits : 0, 3, 4, 5, 8 or 9.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
3 can only be followed by an even number : 30, 32, 34, 36 or 38
4 can only be followed by 2 : 42
5 can only be followed by an odd number : 51, 53, 55, 57, 59
8 can only be followed by an even number : 80, 82, 84, 86 or 88
9 can only be followed by 9 : 99
Also Palindromic Quasipronics of the form x*(x + 2).
Proof by substitution whereby x equals  n – 1 
x * ( x + 2 ) =
      (n – 1) * ( (n – 1) + 2 ) =
      (n – 1) * (n + 1) =
      n2 + n –n – 1 =
n2 – 1 [ QED ]

Decremented Squares of the form x2 – 2 can only start or end with a 2, 3, 4, 7, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
2 can only be followed by an even number : 20, 22, 24, 26 or 28
3 can only be followed by 2 : 32
4 can only be followed by an odd number : 41, 43, 45, 47 or 49
7 can only be followed by an even number : 70, 72, 74, 76 or 78
8 can only be followed by 9 : 89
9 can only be followed by an odd number : 91, 93, 95, 97 or 99

Decremented Squares of the form x2 – 3 can only start or end with a 1, 2, 3, 6, 7 or 8.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
2 can only be followed by 2 : 22
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
6 can only be followed by an even number : 60, 62, 64, 66 or 68
7 can only be followed by 9 : 79
8 can only be followed by an odd number : 81, 83, 85, 87 or 89

Decremented Squares of the form x2 – 4 can only end with a 0, 1, 2, 5, 6 or 7.
And if it terminates in 1, it terminates in 21; if it terminates in 6, it terminates in 96 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
1 can only be followed by 2 : 12
2 can only be followed by an odd number : 21, 23, 25, 27 or 29
5 can only be followed by an even number : 50, 52, 54, 56 or 58
6 can only be followed by 9 : 69
7 can only be followed by an odd number : 71, 73, 75, 77 or 79
Also Palindromic Quasipronics of the form x*(x + 4).
Proof by substitution whereby x equals  n – 2 
x * ( x + 4 ) =
      (n – 2) * ( (n – 2) + 4 ) =
      (n – 2) * (n + 2) =
      n2 + 2n –2n – 4 =
n2 – 4 [ QED ]

Decremented Squares of the form x2 – 5 can only start or end with a 0, 1, 4, 5, 6 or 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by 9 : 59
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
9 can only be followed by an odd number : 91, 93, 95, 97 or 99

Decremented Squares of the form x2 – 6 can only start or end with a 0, 3, 4, 5, 8 or 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as they are never divisible by 11.
3 can only be followed by an even number : 30, 32, 34, 36 or 38 { This 36... produces ever expanding Mandelbrot-like infinite palindromes }
4 can only be followed by 9 : 49
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
8 can only be followed by an odd number : 81, 83, 85, 87 or 89
9 can only be followed by 1 : 91

Decremented Squares of the form x2 – 7 can only start or end with a 2, 3, 4, 7, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
2 can only be followed by an even number : 20, 22, 24, 26 or 28
3 can only be followed by 9 : 39
4 can only be followed by an odd number : 41, 43, 45, 47 or 49
7 can only be followed by an odd number : 71, 73, 75, 77 or 79
8 can only be followed by 1 : 81
9 can only be followed by an even number : 90, 92, 94, 96 or 98

Decremented Squares of the form x2 – 8 can only start or end with a 1, 2, 3, 6, 7 or 8.
Even length palindromes of this form are not possible as they are never divisible by 11.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
2 can only be followed by 9 : 29
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
7 can only be followed by 1 : 71
8 can only be followed by an even number : 80, 82, 84, 86 or 88

Decremented Squares of the form x2 – 9 can only start or end with a 0, 1, 2, 5, 6 or 7.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by 9 : 19
2 can only be followed by an odd number : 21, 23, 25, 27 or 29
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
6 can only be followed by 1 : 61
7 can only be followed by an even number : 70, 72, 74, 76 or 78
Also Palindromic Quasipronics of the form x*(x + 6).
Proof by substitution whereby x equals  n – 3 
x * ( x + 6 ) =
      (n – 3) * ( (n – 3) + 6 ) =
      (n – 3) * (n + 3) =
      n2 + 3n –3n – 9 =
n2 – 9 [ QED ]


An infinite palindromic pattern hides in the list for case n^2 – 2

302 2 = 898
3002 2 = 89998
30002 2 = 8999998
300002 2 = 899999998
3000002 2 = 89999999998
30000002 2 = 8999999999998
300000002 2 = 899999999999998

Two infinite palindromic pattern hide in the list for case n^2 – 3

292 3 = 838
2992 3 = 89398
29992 3 = 8993998
299992 3 = 899939998
2999992 3 = 89999399998
29999992 3 = 8999993999998
299999992 3 = 899999939999998
122 3 = 141
1022 3 = 10401
10022 3 = 1004001
100022 3 = 100040001
1000022 3 = 10000400001
10000022 3 = 1000004000001
100000022 3 = 100000040000001

One finite palindromic pattern starting from length 15 !

281111102 3 = 790234505432097
2811111102 3 = 79023456165432097
28111111102 3 = 7902345672765432097
281111111102 3 = 790234567838765432097
2811111111102 3 = 79023456789498765432097

Four infinite palindromic pattern (probably more) hides in the list for case n^2 – 6

19132 6 = 3659563
190132 6 = 361494163
1900132 6 = 36104940163
19000132 6 = 3610049400163
190000132 6 = 361000494000163
1900000132 6 = 36100004940000163
1910872 6 = 36514241563
190109872 6 = 361417626714163
19001099872 6 = 3610417962697140163
1900010999872 6 = 36100417996269971400163
190000109999872 6 = 361000417999626999714000163
19000001099999872 6 = 3610000417999962699997140000163

This infinite palindromic pattern clean starting from length 19 !

19108913 [365150556041563] {L=15} Alas! Not palindromic but a NEAR MISS
19010890132 6 = 3614139435349314163 {L=19}
1900108900132 6 = 36104138323532383140163 {L=23}
190001089000132 6 = 361004138212353212831400163 {L=27}
19000010890000132 6 = 3610004138201235321028314000163 {L=31}
1900000108900000132 6 = 36100004138200123532100283140000163 {L=35}
190000001089000000132 6 = 361000004138200012353210002831400000163 {L=39}

This infinite palindromic pattern clean starting from length 25 !

1910989132 6 = 36518794549781563 {L=17}
19010989013 [361417703252406714163] {L=21} Alas! Not palindromic but a NEAR MISS
19001098900132 6 = 3610417594125214957140163 {L=25}
1900010989000132 6 = 36100417583212521238571400163 {L=29}
190000109890000132 6 = 361000417582121252121285714000163 {L=33}
19000001098900000132 6 = 3610000417582012125212102857140000163 {L=37}
1900000010989000000132 6 = 36100000417582001212521210028571400000163 {L=41}
190000000109890000000132 6 = 361000000417582000121252121000285714000000163 {L=45}
19000000001098900000000132 6 = 3610000000417582000012125212100002857140000000163 {L=49}
1900000000010989000000000132 6 = 36100000000417582000001212521210000028571400000000163 {L=53}

An infinite palindromic pattern hides in the list for case n^2 – 7

202 7 = 393
2002 7 = 39993
20002 7 = 3999993
200002 7 = 399999993
2000002 7 = 39999999993
20000002 7 = 3999999999993
200000002 7 = 399999999999993

A finite palindromic pattern with only four steps

1(63)2 7 = 26562
1(63)(63)2 7 = 267747762
1(63)(63)(63)2 7 = 2677683867762
1(63)(63)(63)(63)2 7 = 26776859295867762

Two infinite palindromic pattern hide in the list for case n^2 – 8

192 8 = 353
1992 8 = 39593
19992 8 = 3995993
199992 8 = 399959993
1999992 8 = 39999599993
19999992 8 = 3999995999993
199999992 8 = 399999959999993
132 8 = 161
1032 8 = 10601
10032 8 = 1006001
100032 8 = 100060001
1000032 8 = 10000600001
10000032 8 = 1000006000001
100000032 8 = 100000060000001


The Table


Index Nr BasenumberLength
Palindromic Decremented Squares of form n^2–XLength
up down
Case X = 0
See in-depth webpage about Palindromic Square Numbers
up down
Case X = 1
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+2)
up down
Case X = 2
One can find the regular numbers of the form n2 – 2 at
%N n^2 – 2. under A059100.
The palindromic numbers of the form n2 – 2 are categorised as follows :
%N n^2 – 2 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 2. under A0?????.
40300.000.000.000.00015
89.999.999.999.999.999.999.999.999.99829
40151.051.744.377.76815
22.816.629.479.566.566.597.492.661.82229
3930.000.000.000.00014
899.999.999.999.999.999.999.999.99827
383.000.000.000.00013
8.999.999.999.999.999.999.999.99825
372.736.719.294.29313
7.489.632.495.755.575.942.369.84725
361.434.419.498.75213
2.057.559.298.399.938.929.557.50225
35300.000.000.00012
89.999.999.999.999.999.999.99823
34277.104.474.86312
76.786.889.989.098.998.868.76723
33169.944.971.37812
28.881.293.296.669.239.218.88223
32150.408.075.56812
22.622.589.196.069.198.522.62223
3130.000.000.00011
899.999.999.999.999.999.99821
3020.470.241.05411
419.030.768.808.867.030.91421
2920.414.740.29611
416.761.621.353.126.167.61421
2820.371.679.75411
415.005.335.999.533.500.51421
273.000.000.00010
8.999.999.999.999.999.99819
262.759.060.76310
7.612.416.293.926.142.16719
252.728.091.60710
7.442.483.816.183.842.44719
241.807.133.72510
3.265.732.300.032.375.62319
231.489.076.31810
2.217.348.280.828.437.12219
22314.838.8999
99.123.532.323.532.19917
21300.000.0009
89.999.999.999.999.99817
2030.000.0008
899.999.999.999.99815
1920.367.6968
414.843.040.348.41415
183.000.0007
8.999.999.999.99813
17300.0006
89.999.999.99811
16202.5046
41.007.870.01411
15151.2326
22.871.117.82211
14144.2986
20.821.912.80211
1330.0005
899.999.9989
123.1494
9.916.1997
113.0004
8.999.9987
102.1744
4.726.2747
92.0944
4.384.8347
83003
89.9985
72043
41.6145
6312
9593
5302
8983
4272
7273
331
71
221
21
111
–11
001
–21
up down
Case X = 3
One can find the regular numbers of the form n2 – 3 at
%N n^2 – 3. under A028872.
The palindromic numbers of the form n2 – 3 are categorised as follows :
%N n^2 – 3 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 3. under A0?????.
91299.999.999.999.99915
89.999.999.999.999.399.999.999.999.99829
90257.617.848.652.46315
66.366.955.944.323.332.344.955.966.36629
89187.685.767.311.01615
35.225.947.251.124.842.115.274.952.25329
88177.196.446.108.35415
31.398.580.513.430.803.431.508.589.31329
87111.009.388.950.48215
12.323.084.435.159.395.153.448.032.32129
86100.000.000.000.00215
10.000.000.000.000.400.000.000.000.00129
8529.999.999.999.99914
899.999.999.999.939.999.999.999.99827
8428.927.607.042.87914
836.806.449.227.222.722.944.608.63827
8318.401.474.433.90614
338.614.261.341.696.143.162.416.83327
8215.052.520.152.52514
226.578.362.942.171.249.263.875.62227
8114.843.663.905.69514
220.334.358.145.232.541.853.433.02227
8011.982.083.209.81214
143.570.318.046.858.640.813.075.34127
7910.000.000.000.00214
100.000.000.000.040.000.000.000.00127
786.108.627.042.87613
37.315.324.348.955.984.342.351.37326
774.700.308.259.34513
22.092.897.732.866.823.779.829.02226
762.999.999.999.99913
8.999.999.999.993.999.999.999.99825
752.542.454.379.84313
6.464.074.273.582.853.724.704.64625
741.108.553.389.83213
1.228.890.618.108.018.160.988.22125
731.000.000.000.00213
1.000.000.000.004.000.000.000.00125
72299.999.999.99912
89.999.999.999.399.999.999.99823
71298.530.039.85112
89.120.184.693.439.648.102.19823
70293.254.640.78112
85.998.284.339.593.348.289.95823
69281.111.111.11012
79.023.456.789.498.765.432.09723
68149.088.589.58512
22.227.407.544.444.570.472.22223
67134.952.824.27812
18.212.264.780.608.746.221.28123
66100.000.000.00212
10.000.000.000.400.000.000.00123
6538.318.240.26211
1.468.287.536.776.357.828.64122
6429.999.999.99911
899.999.999.939.999.999.99821
6328.111.111.11011
790.234.567.838.765.432.09721
6210.145.537.69811
102.931.935.181.539.139.20121
6110.000.000.00211
100.000.000.040.000.000.00121
605.748.742.99410
33.048.046.011.064.084.03320
592.999.999.99910
8.999.999.993.999.999.99819
582.811.111.11010
7.902.345.672.765.432.09719
572.578.854.58710
6.650.490.980.890.940.56619
561.485.275.39510
2.206.042.998.992.406.02219
551.104.201.68210
1.219.261.354.531.629.12119
541.038.329.05210
1.078.127.220.227.218.70119
531.000.000.00210
1.000.000.004.000.000.00119
52299.999.9999
89.999.999.399.999.99817
51281.111.1109
79.023.456.165.432.09717
50198.699.8649
39.481.635.953.618.49317
49119.193.8389
14.207.171.017.170.24117
48100.000.0029
10.000.000.400.000.00117
4792.274.8818
8.514.653.663.564.15816
4659.963.8668
3.595.665.225.665.95316
4543.535.7728
1.895.363.443.635.98116
4429.999.9998
899.999.939.999.99815
4328.111.1108
790.234.505.432.09715
4224.544.2978
602.422.515.224.20615
4118.750.5348
351.582.525.285.15315
4010.000.0028
100.000.040.000.00115
399.260.0697
85.748.877.884.75814
389.258.4317
85.718.544.581.75814
378.157.9137
66.551.544.515.56614
363.563.9187
12.701.511.510.72114
353.281.4487
10.767.900.976.70114
342.999.9997
8.999.993.999.99813
331.484.8457
2.204.764.674.02213
321.000.0027
1.000.004.000.00113
31889.1906
790.658.856.09712
30299.9996
89.999.399.99811
29249.3776
62.188.888.12611
28150.5256
22.657.775.62211
27148.5056
22.053.735.02211
26100.0026
10.000.400.00111
2589.3705
7.986.996.89710
2479.3275
6.292.772.92610
2342.8725
1.838.008.38110
2240.9585
1.677.557.76110
2140.4425
1.635.555.36110
2029.9995
899.939.9989
1924.5475
602.555.2069
1812.9585
167.909.7619
1711.8625
140.707.0419
1610.0025
100.040.0019
152.9994
8.993.9987
141.8844
3.549.4537
131.0024
1.004.0017
122993
89.3985
111023
10.4015
10832
6.8864
9382
1.4414
8292
8383
7152
2223
6122
1413
561
332
451
222
331
61
221
11
111
–21
001
–31
up down
Case X = 4
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+4)
One can find the regular numbers of the form n2 – 4 at
%N n^2 – 4. under A028347.
The palindromic numbers of the form n2 – 4 are categorised as follows :
%N n^2 – 4 is a palindrome. under A028555.
%N Palindromes of the form n^2 – 4. under A028556.
111
–31
001
–41
up down
Case X = 5
One can find the regular numbers of the form n2 – 5 at
%N n^2 – 5. under A028875.
The palindromic numbers of the form n2 – 5 are categorised as follows :
%N n^2 – 5 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 5. under A0?????.
58311.724.544.575.57215
97.172.191.690.847.774.809.619.127.17929
57202.050.838.683.80315
40.824.541.412.828.182.821.414.542.80429
5697.888.964.408.30814
9.582.249.352.930.990.392.539.422.85928
5579.518.245.402.17114
6.323.151.351.839.889.381.531.513.23628
5424.376.775.668.35014
594.227.191.985.060.589.191.722.49527
5320.991.089.109.00714
440.625.821.982.272.289.128.526.04427
5212.583.404.092.31614
158.342.058.550.515.055.850.243.85127
516.851.026.560.06313
46.936.564.926.688.662.946.563.96426
503.055.742.940.31213
9.337.564.917.266.627.194.657.33925
492.108.821.814.64313
4.447.129.445.914.195.449.217.44425
48682.055.723.83712
465.200.010.418.814.010.002.56424
47315.458.954.59812
99.514.352.036.063.025.341.59923
46309.549.710.80812
95.821.023.461.316.432.012.85923
45303.103.448.76812
91.871.700.655.055.600.717.81923
44251.972.689.52112
63.490.236.264.446.263.209.43623
43209.910.890.99312
44.062.582.157.475.128.526.04423
42140.638.946.71412
19.779.313.332.823.331.397.79123
41131.073.116.27612
17.180.161.810.301.816.108.17123
4098.841.904.32211
9.769.722.049.999.402.279.67922
3979.408.330.07111
6.305.682.884.664.882.865.03622
3831.283.616.87811
978.664.684.969.486.466.87921
3730.629.582.06211
938.171.297.292.792.171.83921
3624.849.903.93911
617.517.725.777.527.715.71621
3524.468.311.87011
598.698.285.767.582.896.89521
3420.990.990.99311
440.621.702.868.207.126.04421
3312.252.321.91611
150.119.392.333.293.911.05121
327.820.800.73910
61.164.924.199.142.946.11620
313.092.785.89210
9.565.324.573.754.235.65919
302.435.714.18010
5.932.703.566.653.072.39519
292.099.109.00710
4.406.258.623.268.526.04419
281.397.314.18610
1.952.486.934.396.842.59119
271.053.649.04610
1.110.176.312.136.710.11119
26210.900.8939
44.479.186.668.197.44417
2564.942.1238
4.217.479.339.747.12416
2421.089.1078
444.750.434.057.44415
2320.990.9938
440.621.787.126.04415
222.628.8517
6.910.857.580.19613
212.436.4207
5.936.142.416.39513
20978.5426
957.544.445.75912
19783.3616
613.654.456.31612
18252.3796
63.695.159.63611
17210.8936
44.475.857.44411
1677.3705
5.986.116.89510
1569.4835
4.827.887.28410
1421.6135
467.121.7649
1310.6965
114.404.4119
123.6564
13.366.3318
112.4404
5.953.5957
101.1564
1.336.3317
94363
190.0916
82593
67.0765
7812
6.5564
6142
1913
571
442
441
112
331
41
221
–11
111
–41
001
–51
up down
Case X = 6
One can find the regular numbers of the form n2 – 6 at
%N n^2 – 6. under A028878.
The palindromic numbers of the form n2 – 6 are categorised as follows :
%N n^2 – 6 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 6. under A0?????.
51302.142.579.927.31515
91.290.138.605.133.933.150.683.109.21929
50296.255.835.953.97215
87.767.520.336.786.768.763.302.576.77829
49190.001.098.900.01315
36.100.417.583.212.521.238.571.400.16329
48190.000.000.000.01315
36.100.000.000.004.940.000.000.000.16329
4730.274.870.968.87514
916.567.812.182.030.281.218.765.61927
4630.166.868.936.75514
910.039.981.447.353.744.189.930.01927
4519.001.089.109.98714
361.041.387.365.666.563.783.140.16327
4419.000.108.900.01314
361.004.138.212.353.212.831.400.16327
4319.000.010.999.98714
361.000.417.999.626.999.714.000.16327
4219.000.000.000.01314
361.000.000.000.494.000.000.000.16327
411.900.109.890.01313
3.610.417.594.125.214.957.140.16325
401.900.000.000.01313
3.610.000.000.049.400.000.000.16325
39227.544.887.93912
51.776.676.027.172.067.667.71523
38226.152.547.98912
51.144.974.961.916.947.944.11523
37221.502.874.81012
49.063.523.549.094.532.536.09423
36190.108.910.98712
36.141.398.036.663.089.314.16323
35190.010.890.01312
36.104.138.323.532.383.140.16323
34190.001.099.98712
36.100.417.996.269.971.400.16323
33190.000.000.01312
36.100.000.004.940.000.000.16323
32181.584.343.07712
32.972.873.650.705.637.827.92323
3130.181.812.65511
910.941.815.141.518.149.01921
3029.634.602.12211
878.209.642.929.246.902.87821
2924.452.608.65111
597.930.069.838.960.039.79521
2819.000.000.01311
361.000.000.494.000.000.16321
272.988.003.95210
8.928.167.617.167.618.29819
261.901.089.01310
3.614.139.435.349.314.16319
251.900.109.98710
3.610.417.962.697.140.16319
241.900.000.01310
3.610.000.049.400.000.16319
23191.098.9139
36.518.794.549.781.56317
22190.000.0139
36.100.004.940.000.16317
2129.848.3488
890.923.878.329.09815
2022.213.8808
493.456.464.654.39415
1919.010.9878
361.417.626.714.16315
1819.000.0138
361.000.494.000.16315
172.930.6927
8.588.955.598.85813
162.316.1297
5.364.453.544.63513
152.220.5207
4.930.709.070.39413
141.900.7637
3.612.899.982.16313
131.900.0137
3.610.049.400.16313
12302.1356
91.285.558.21911
11191.0876
36.514.241.56311
10190.0136
36.104.940.16311
930.2755
916.575.6199
819.0135
361.494.1639
72.2614
5.112.1157
61.9134
3.659.5637
51.8574
3.448.4437
42923
85.2585
331
31
221
–21
111
–51
001
–61
up down
Case X = 7
One can find the regular numbers of the form n2 – 7 at
%N n^2 – 7. under A028881.
The palindromic numbers of the form n2 – 7 are categorised as follows :
%N n^2 – 7 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 7. under A0?????.
78307.703.972.678.78415
94.681.734.802.305.850.320.843.718.64929
77303.842.998.768.34415
92.320.567.900.539.893.500.976.502.32929
76279.001.098.900.12215
77.841.613.187.475.657.478.131.614.87729
75217.750.934.842.30915
47.415.469.624.699.499.642.696.451.47429
74208.939.304.470.62915
43.655.632.952.670.207.625.923.655.63429
73208.417.441.681.52115
43.437.829.997.070.207.079.992.873.43429
72200.000.000.000.00015
39.999.999.999.999.999.999.999.999.99329
7127.900.010.999.87814
778.410.613.793.313.397.316.014.87727
7022.217.531.211.79914
493.618.693.147.262.741.396.816.39427
6920.000.000.000.00014
399.999.999.999.999.999.999.999.99327
6815.689.702.164.40714
246.166.754.007.797.700.457.661.64227
673.010.534.949.20413
9.063.320.680.378.730.860.233.60925
662.847.385.777.70513
8.107.605.767.076.707.675.067.01825
652.790.109.890.12213
7.784.713.198.956.598.913.174.87725
642.000.000.000.00013
3.999.999.999.999.999.999.999.99325
631.674.399.042.96713
2.803.612.155.088.805.512.163.08225
621.640.692.403.06313
2.691.871.561.468.641.651.781.96225
611.438.749.187.14713
2.069.999.223.516.153.229.999.60225
601.416.714.309.24713
2.007.079.434.025.204.349.707.00225
59285.129.510.43512
81.298.837.720.902.773.889.21823
58279.001.099.87812
77.841.613.733.133.731.614.87723
57200.000.000.00012
39.999.999.999.999.999.999.99323
56198.455.185.22012
39.384.460.540.704.506.448.39323
55197.644.202.69012
39.063.230.856.965.803.236.09323
54169.804.109.16712
28.833.435.489.998.453.433.88223
5331.372.742.13611
984.248.949.131.949.842.48921
5220.000.000.00011
399.999.999.999.999.999.99321
5116.870.518.06711
284.614.379.848.973.416.48221
5014.895.699.37711
221.881.859.929.958.188.12221
492.790.109.87810
7.784.713.131.313.174.87719
482.088.111.87110
4.360.211.185.811.120.63419
472.048.625.66110
4.196.867.098.907.686.91419
462.000.000.00010
3.999.999.999.999.999.99319
451.508.870.97310
2.276.691.613.161.966.72219
441.417.005.75310
2.007.905.304.035.097.00219
43271.226.1129
73.563.603.830.636.53717
42222.706.4499
49.598.162.426.189.59417
41200.000.0009
39.999.999.999.999.99317
40163.636.3639
26.776.859.295.867.76217
39161.682.7639
26.141.315.851.314.16217
38148.953.1279
22.187.034.043.078.12217
3728.495.9858
812.021.161.120.21815
3627.791.2228
772.352.020.253.27715
3520.000.0008
399.999.999.999.99315
342.850.1157
8.123.155.513.21813
332.787.9727
7.772.787.872.77713
322.780.2227
7.729.634.369.27713
312.143.7817
4.595.796.975.95413
302.000.0007
3.999.999.999.99313
291.996.6307
3.986.531.356.89313
281.636.3637
2.677.683.867.76213
271.569.8437
2.464.407.044.64213
26212.9816
45.360.906.35411
25200.0006
39.999.999.99311
2427.1125
735.060.5379
2326.6825
711.929.1179
2220.0005
399.999.9939
2116.3635
267.747.7629
2015.5575
242.020.2429
192.0794
4.322.2347
182.0394
4.157.5147
172.0004
3.999.9937
161.6374
2.679.7627
161.5574
2.424.2427
153143
98.5895
142853
81.2185
132783
77.2775
122683
71.8175
112003
39.9935
101633
26.5625
91573
24.6425
8282
7773
7212
4343
6202
3933
5172
2823
441
91
331
21
221
–31
111
–61
001
–71
up down
Case X = 8
One can find the regular numbers of the form n2 – 8 at
%N n^2 – 8. under A028884.
The palindromic numbers of the form n2 – 8 are categorised as follows :
%N n^2 – 8 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 8. under A0?????.
65199.999.999.999.99915
39.999.999.999.999.599.999.999.999.99329
64193.511.242.945.80915
37.446.601.146.431.913.464.110.664.47329
63181.886.803.762.17915
33.082.809.382.821.412.828.390.828.03329
62170.530.193.287.41015
29.080.546.822.641.414.622.864.508.09229
61130.122.803.816.31315
16.931.944.073.018.681.037.044.913.96129
60129.566.082.859.86315
16.787.369.827.648.884.672.896.378.76129
59100.000.000.000.00315
10.000.000.000.000.600.000.000.000.00129
5825.646.720.121.54214
657.754.252.992.707.299.252.457.75627
5719.999.999.999.99914
399.999.999.999.959.999.999.999.99327
5619.795.435.332.14914
391.859.259.989.292.989.952.958.19327
5518.339.849.698.37114
336.350.086.958.838.859.680.053.63327
5410.000.000.000.00314
100.000.000.000.060.000.000.000.00127
532.831.774.899.45413
8.018.949.081.177.711.809.498.10825
522.676.770.480.12513
7.165.100.203.268.623.020.015.61725
512.675.894.320.37513
7.160.410.413.815.183.140.140.61725
501.999.999.999.99913
3.999.999.999.995.999.999.999.99325
491.839.867.157.47113
3.385.111.157.140.417.511.115.83325
481.010.273.888.29713
1.020.653.329.374.739.233.560.20125
471.000.000.000.00313
1.000.000.000.006.000.000.000.00125
46293.795.842.87612
86.315.997.291.219.279.951.36823
45266.623.495.19512
71.088.088.189.998.188.088.01723
44199.999.999.99912
39.999.999.999.599.999.999.99323
43173.192.892.40012
29.995.777.977.877.977.759.99223
42100.000.000.00312
10.000.000.000.600.000.000.00123
4119.999.999.99911
399.999.999.959.999.999.99321
4019.295.962.59111
372.334.172.313.271.433.27321
3910.000.000.00311
100.000.000.060.000.000.00121
381.999.999.99910
3.999.999.995.999.999.99319
371.000.000.00310
1.000.000.006.000.000.00119
36286.740.1069
82.219.888.388.891.22817
35264.570.0029
69.997.285.958.279.99617
34199.999.9999
39.999.999.599.999.99317
33173.201.7009
29.998.828.882.889.99217
32127.813.0379
16.336.172.427.163.36117
31100.000.0039
10.000.000.600.000.00117
3029.731.0868
883.937.474.739.38815
2919.999.9998
399.999.959.999.99315
2810.000.0038
100.000.060.000.00115
272.871.2947
8.244.329.234.42813
261.999.9997
3.999.995.999.99313
251.211.5937
1.467.957.597.64113
241.184.2577
1.402.464.642.04113
231.121.9777
1.258.832.388.52113
221.000.0037
1.000.006.000.00113
21286.5566
82.114.341.12811
20199.9996
39.999.599.99311
19120.8436
14.603.030.64111
18100.0036
10.000.600.00111
1728.3545
803.949.3089
1619.9995
399.959.9939
1519.2595
370.909.0739
1417.2705
298.252.8929
1310.0035
100.060.0019
122.5124
6.310.1367
111.9994
3.995.9937
101.3674
1.868.6817
91.1934
1.423.2417
81.0034
1.006.0017
71993
39.5935
61033
10.6015
5192
3533
4132
1613
441
81
331
11
221
–41
111
–71
001
–81
up down
Case X = 9
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+6)
One can find the regular numbers of the form n2 – 9 at
%N n^2 – 9. under A028560.
The palindromic numbers of the form n2 – 9 are categorised as follows :
%N n^2 – 9 is a palindrome. under A0?????.
%N Palindromes of the form n^2 – 9. under A0?????.
222
–53
112
–83
001
–91




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