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Details of Palindromic Triangulars
[1] upto [49]
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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.


Factorizations

back [49]
F_ba  34456434 =
      2  x  3  x  787  x  7297
F_pt  593622939226395 =
      5  x  13  x  37  x  14327

back [48]
F_ba  33062934 =
      2  x  3  x  5510489
F_pt  546578818875645 =
      5  x  97  x  68171

back [47]
F_ba  32850970 =
      2  x  5  x  17  x  173  x  1117
F_pt  539593131395935 =
      67  x  490313

back [46]
F_ba  31643910 =
      2  x  3  x  3  x  5  x  351599
F_pt  500668535866005 =
      13  x  19  x  128113

back [45]
F_ba  26743422 =
      2  x  3  x  727  x  6131
F_pt  357605323506753 =
      7  x  29  x  47  x  2803

back [44]
F_ba  15126258 =
      2  x  3  x  7  x  139  x  2591
F_pt  114401848104411 =
      2309  x  6551

back [43]
F_ba  12812392 =
      2  x  2  x  2  x  113  x  14173
F_pt  82078700787028 =
      11  x  31  x  37573

back [42]
F_ba  11631048 =
      2  x  2  x  2  x  3  x  11  x  13  x  3389
F_pt  67640644604676 =
      167  x  257  x  271

back [41]
F_ba  11111111 = PALINDROMIC
      11  x  73  x  101  x  137
F_pt  61728399382716 =
      2  x  2  x  3  x  3  x  154321

back [40]
F_ba  6307938 =
      2  x  3  x  3  x  7  x  13  x  3851
F_pt  19895044059891 =
      11  x  109  x  5261

back [39]
F_ba  3707883 =
      3  x  3  x  3  x  191  x  719
F_pt  6874200024786 =
      2  x  926971

Divide the basenumber into groups of three and add them up : 003 + 707 + 883 = 1593 1593 is the basenumber of palindromic triangular [16] The sum of the factors of the basenumbers add up to a palindrome : 3 + 3 + 3 + 191 + 719 = 919
back [38] F_ba 3457634 = 2 x 101 x 17117 F_pt 5977618167795 = 3 x 5 x 353 x 653 back [37] F_ba 3240425 = 5 x 5 x 227 x 571 F_pt 5250178710525 = 3 x 7 x 77153
The sum of the factors of the basenumbers add up to a palindrome : 5 + 5 + 227 + 571 = 808
back [36] F_ba 1620621 = 3 x 3 x 3 x 193 x 311 F_pt 1313207023131 = 107 x 7573 back [35] F_ba 417972 = 2 x 2 x 3 x 61 x 571 F_pt 87350505378 = 31 x 97 x 139 back [34] F_ba 365436 = 2 x 2 x 3 x 3 x 10151 F_pt 66771917766 = 71 x 5147 back [33] F_ba 342270 = 2 x 3 x 3 x 5 x 3803 F_pt 58574547585 = 31 x 61 x 181 back [32] F_ba 337650 = 2 x 3 x 5 x 5 x 2251 F_pt 57003930075 = 337651 back [31] F_ba 246642 = PALINDROMIC 2 x 3 x 11 x 37 x 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 [30] F_ba 179158 = 2 x 7 x 67 x 191 F_pt 16048884061 = 97 x 1847
Separate the basenumber into two parts of three digits each and multiply them : 179 x 158 = 28282 which is a palindrome !
back [29] F_ba 167053 = 89 x 1877 F_pt 13953435931 = 101 x 827 back [28] F_ba 111111 = PALINDROMIC 3 x 7 x 11 x 13 x 37 F_pt 6172882716 = 2 x 2 x 17 x 19 x 43 back [27] F_ba 102849 = 3 x 34283 F_pt 5289009825 = 5 x 5 x 11 x 11 x 17 back [26] F_ba 57166 = 2 x 101 x 283 F_pt 1634004361 = 11 x 5197 back [25] F_ba 50281 = 7 x 11 x 653 F_pt 1264114621 = 31 x 811 back [24] F_ba 18906 = 2 x 3 x 23 x 137 F_pt 178727871 = 7 x 37 x 73 back [23] F_ba 11088 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 11 F_pt 61477416 = 13 x 853 back [22] F_ba 8382 = 2 x 3 x 11 x 127 F_pt 35133153 = 83 x 101 back [21] F_ba 3548 = 2 x 2 x 887 F_pt 6295926 = 3 x 7 x 13 x 13 back [20] F_ba 3369 = 3 x 1123 F_pt 5676765 = 5 x 337 back [19] F_ba 3185 = 5 x 7 x 7 x 13 F_pt 5073705 = 3 x 3 x 3 x 59 back [18] F_ba 2662 = PALINDROMIC 2 x 11 x 11 x 11 F_pt 3544453 = 2663 back [17] F_ba 1833 = 3 x 13 x 47 F_pt 1680861 = 7 x 131 back [16] F_ba 1593 = 3 x 3 x 3 x 59 F_pt 1269621 = 797 back [15] F_ba 1287 = 3 x 3 x 11 x 13 F_pt 828828 = 2 x 2 x 7 x 23 back [14] F_ba 1111 = PALINDROMIC 11 x 101 F_pt 617716 = 2 x 2 x 139 back [13] F_ba 363 = PALINDROMIC 3 x 11 x 11 F_pt 66066 = 2 x 7 x 13 back [12] F_ba 173 = PRIME 173 F_pt 15051 = 3 x 29 back [11] F_ba 132 = 2 x 2 x 3 x 11 F_pt 8778 = 7 x 19 back [10] F_ba 109 = PRIME 109 F_pt 5995 = 5 x 11 back [9] F_ba 77 = PALINDROMIC 7 x 11 F_pt 3003 = 3 x 13 back [8] F_ba 36 = 2 x 2 x 3 x 3 F_pt 666 = 37 back [7] F_ba 34 = 2 x 17 F_pt 595 = 5 x 7 back [6] F_ba 18 = 2 x 3 x 3 F_pt 171 = 19 back [5] F_ba 11 = PALINDROMIC PRIME 11 F_pt 66 = 2 x 3 back [4] F_ba 10 = 2 x 5 F_pt 55 = 11 back [3] F_ba 3 = PALINDROMIC PRIME 3 F_pt 6 = 2 back [2] F_ba 2 = PALINDROMIC PRIME 2 F_pt 3 = 3 back [1] F_ba 1 = PALINDROMIC 1 F_pt 1 = 1 back [0] F_ba 0 = 0 F_pt 0 = 0
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