A125770 First occurrence of n in A125769.

1, 2, 7, 9, 34, 31, 54, 15, 16, 26, 148, 68, 398, 62, 193, 25, 27, 140, 550, 397, 107, 113, 50, 122, 950, 226, 38, 169, 40, 562, 187, 44, 327, 763, 70, 211, 362, 49, 1726, 79, 394, 153, 55, 202, 1600, 125, 61, 419, 94, 95, 225, 98, 66, 1036, 508, 1298, 983, 69, 71

Offset: 1

Author

Jonathan Vos Post and Robert G. Wilson v, Dec 03 2006

Keywords

• nonn

Comments

If we restrict ourselves to just j*T_k +1 or j*T_k -1 then there are values which do not occur. As an example if the minus is used then 8 and 9 are missing.

Crossrefs

A125769 = a(n) is the least number j such that j*T_k +/- 1 is n-th prime for some k-th triangular number.

Cf. A000217, A125765, A125766, A125767, A125768, A125769.

Programs

Mathematica

triQ[n_] := IntegerQ@ Sqrt[8*n + 1]; f[n_] := Block[{j = 1, p = Prime@n}, While[ !triQ[(p - 1)/j] && !triQ[(p + 1)/j], j++ ]; j]; t = Table[0, {100}]; Do[ a = f@n; If[a < 101 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 3500}]; t