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Details of Palindromic Triangulars
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Legend


F_ba  Decomposition of the basenumber in its prime factors.
F_pt  Decomposition of the palindromic triangular.
      Note : a palindromic triangular will always be divisible by its basenumber when this
             last one is 'odd'. With 'even' basenumbers you'll notice that the triangulars
             are always divisible by half their basenumbers.
             To reconstruct the triangular you must take into account the green together with
             the purple prime factors but not the black 2.
Date  Date of discovery by the author.
blue     Hypertext links to related topics in number theory 
Comm  Comments about the palindromic triangular number.


Factorization


back [49]
F_ba  33062934 =
      2 * 3 * 5510489
F_pt  546578818875645 =
      5 * 97 * 68171

back [48]
F_ba  32850970 =
      2 * 5 * 17 * 173 * 1117
F_pt  539593131395935 =
      67 * 490313

back [47]
F_ba  31643910 =
      2 * 3 * 3 * 5 * 351599
F_pt  500668535866005 =
      13 * 19 * 128113

back [46]
F_ba  26743422 =
      2 * 3 * 727 * 6131
F_pt  357605323506753 =
      7 * 29 * 47 * 2803

back [45]
F_ba  15126258 =
      2 * 3 * 7 * 139 * 2591
F_pt  114401848104411 =
      2309 * 6551

back [44]
F_ba  12812392 =
      2 * 2 * 2 * 113 * 14173
F_pt  82078700787028 =
      11 * 31 * 37573

back [43]
F_ba  11631048 =
      2 * 2 * 2 * 3 * 11 * 13 * 3389
F_pt  67640644604676 =
      167 * 257 * 271

back [42]
F_ba  11111111 = PALINDROMIC
      11 * 73 * 101 * 137
F_pt  61728399382716 =
      2 * 2 * 3 * 3 * 154321

back [41]
F_ba  6307938 =
      2 * 3 * 3 * 7 * 13 * 3851
F_pt  19895044059891 =
      11 * 109 * 5261

back [40]
F_ba  3707883 =
      3 * 3 * 3 * 191 * 719
F_pt  6874200024786 =
      2 * 926971

Divide the basenumber into groups of three and add them up :
003 + 707 + 883 = 1593
1593 is the basenumber of palindromic triangular [17]

The sum of the factors of the basenumbers add up to a palindrome :
3 + 3 + 3 + 191 + 719 =  919 



back [39]
F_ba  3457634 =
      2 * 101 * 17117
F_pt  5977618167795 =
      3 * 5 * 353 * 653

back [38]
F_ba  3240425 =
      5 * 5 * 227 * 571
F_pt  5250178710525 =
      3 * 7 * 77153

The sum of the factors of the basenumbers add up to a palindrome :
5 + 5 + 227 + 571 =  808 



back [37]
F_ba  1620621 =
      3 * 3 * 3 * 193 * 311
F_pt  1313207023131 =
      107 * 7573

back [36]
F_ba  417972 =
      2 * 2 * 3 * 61 * 571
F_pt  87350505378 =
      31 * 97 * 139

back [35]
F_ba  365436 =
      2 * 2 * 3 * 3 * 10151
F_pt  66771917766 =
      71 * 5147

back [34]
F_ba  342270 =
      2 * 3 * 3 * 5 * 3803
F_pt  58574547585 =
      31 * 61 * 181

back [33]
F_ba  337650 =
      2 * 3 * 5 * 5 * 2251
F_pt  57003930075 =
      337651

back [32]
F_ba  246642 = PALINDROMIC
      2 * 3 * 11 * 37 * 101
F_pt  30416261403 =
      246643

The string  30416261403  was found at position 36111197
counting from the first digit after the decimal point. The 3. is not counted.
The Pi-Search Page now serving 200.000.000 digits



back [31]
F_ba  179158 =
      2 * 7 * 67 * 191
F_pt  16048884061 =
      97 * 1847

Separate the basenumber into two parts of three digits each and multiply them :
179 x 158 =  28282  which is a palindrome !



back [30]
F_ba  167053 =
      89 * 1877
F_pt  13953435931 =
      101 * 827

back [29]
F_ba  111111 = PALINDROMIC
      3 * 7 * 11 * 13 * 37
F_pt  6172882716 =
      2 * 2 * 17 * 19 * 43

back [28]
F_ba  102849 =
      3 * 34283
F_pt  5289009825 =
      5 * 5 * 11 * 11 * 17

back [27]
F_ba  57166 =
      2 * 101 * 283
F_pt  1634004361 =
      11 * 5197

back [26]
F_ba  50281 =
      7 * 11 * 653
F_pt  1264114621 =
      31 * 811

back [25]
F_ba  18906 =
      2 * 3 * 23 * 137
F_pt  178727871 =
      7 * 37 * 73

back [24]
F_ba  11088 =
      2 * 2 * 2 * 2 * 3 * 3 * 7 * 11
F_pt  61477416 =
      13 * 853

back [23]
F_ba  8382 =
      2 * 3 * 11 * 127
F_pt  35133153 =
      83 * 101

back [22]
F_ba  3548 =
      2 * 2 * 887
F_pt  6295926 =
      3 * 7 * 13 * 13

back [21]
F_ba  3369 =
      3 * 1123
F_pt  5676765 =
      5 * 337

back [20]
F_ba  3185 =
      5 * 7 * 7 * 13
F_pt  5073705 =
      3 * 3 * 3 * 59

back [19]
F_ba  2662 = PALINDROMIC
      2 * 11 * 11 * 11
F_pt  3544453 =
      2663

back [18]
F_ba  1833 =
      3 * 13 * 47
F_pt  1680861 =
      7 * 131

back [17]
F_ba  1593 =
      3 * 3 * 3 * 59
F_pt  1269621 =
      797

back [16]
F_ba  1287 =
      3 * 3 * 11 * 13
F_pt  828828 =
      2 * 2 * 7 * 23

back [15]
F_ba  1111 = PALINDROMIC
      11 * 101
F_pt  617716 =
      2 * 2 * 139

back [14]
F_ba  363 = PALINDROMIC
      3 * 11 * 11
F_pt  66066 =
      2 * 7 * 13

back [13]
F_ba  173 = PRIME
      173
F_pt  15051 =
      3 * 29

back [12]
F_ba  132 =
      2 * 2 * 3 * 11
F_pt  8778 =
      7 * 19

back [11]
F_ba  109 = PRIME
      109
F_pt  5995 =
      5 * 11

back [10]
F_ba  77 = PALINDROMIC
      7 * 11
F_pt  3003 =
      3 * 13

back [9]
F_ba  36 =
      2 * 2 * 3 * 3
F_pt  666 =
      37

back [8]
F_ba  34 =
      2 * 17
F_pt  595 =
      5 * 7

back [7]
F_ba  18 =
      2 * 3 * 3
F_pt  171 =
      19

back [6]
F_ba  11 = PALINDROMIC PRIME
      11
F_pt  66 =
      2 * 3

back [5]
F_ba  10 =
      2 * 5
F_pt  55 =
      11

back [4]
F_ba  3 = PALINDROMIC PRIME
      3
F_pt  6 =
      2

back [3]
F_ba  2 = PALINDROMIC PRIME
      2
F_pt  3 =
      3

back [2]
F_ba  1 = PALINDROMIC
      1
F_pt  1 =
      1

back [1]
F_ba  0 = PALINDROMIC
      0
F_pt  0 =
      0

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