## S000803

Triangle whose n-th row has the numbers m such that there is an m-gonal number equal to A063778(n).

3, 3, 6, 3, 6, 15, 3, 4, 13, 36, 4, 8, 24, 76, 225, 3, 6, 12, 39, 188, 561, 3, 4, 6, 29, 60, 124, 1225, 3, 10, 22, 133, 267, 570, 1195, 11935, 3, 6, 8, 58, 216, 329, 787, 3928, 11781, 7, 16, 48, 80, 181, 303, 763, 2742, 9136, 27405, 3, 285, 316, 373, 586, 1293

1

A063778(n) is the first number that occurs in n m-gonal sequences. This sequence lists those n numbers. See S000804 for the locations of these numbers in the m-gonal sequences.

T. D. Noe, Plot of 27 rows

T. D. Noe, Table of 27 rows

Eric W. Weisstein, MathWorld: Polygonal Number

(Mma) s = {3, 6, 15, 36, 225, 561, 1225, 11935, 11781, 27405, 220780, 203841, 3368925, 4921840, 7316001, 33631521, 142629201, 879207616, 1383958576, 3800798001, 12524486976, 181285005825, 118037679760, 239764947345, 738541591425, 1289707733601, 1559439365121}; k =.; f =.; q = Table[sol = Reduce[k ((f - 2) k - (f - 4))/2 == s[[n]] && k > 0, {f, k}, Integers]; {Table[sol[[i, 1, 2]], {i, 2, Length[sol]}], Table[sol[[i, 2, 2]], {i, 2, Length[sol]}]}, {n, Length[s]}]; Transpose[q][[1]]

Cf. A063778, S000804.

nonn,tabl

T. D. Noe, Dec 17 2015