A125768 Least number k such that n*T_k +/- 1 is prime.

1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 2, 3, 1, 3, 1, 4, 1, 3, 2, 3, 1, 3, 1, 3, 1, 4, 1, 3, 1, 3, 1, 3, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 3, 1, 3, 1, 3, 2, 3, 1, 3, 1, 4, 1, 4, 1, 3, 1, 3, 2, 3, 1, 7, 1, 3, 1, 3, 1, 3, 2, 3, 1, 8, 1, 3, 2, 3, 2, 3, 1, 4, 1, 3, 1, 3, 1, 3, 1, 3

Offset: 1

Author

Jonathan Vos Post & Robert G. Wilson v, Dec 01 2006

Keywords

• nonn

Comments

k times the n-th triangular number plus or minus 1 is prime.

Eventually every prime p appears since (p +/-1) times 1(1+1)/2 equals (p +/- 1).

The first occurrence of k: 1, 26, 5, 31, 320, 698, 79, 89, 1058, 7404, 223, 299, 8504, 13630, 845, 1217, 3334, 26074, 2349, 1835, 71926, 111616, 2473, 1189, 27754, 140366, 3709, 4109, 250126, 223078, 30359, 9649, ...,.

Crossrefs

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

Programs

Mathematica

f[n_] := Block[{k = 1, trnglr = n*k(k + 1)/2}, While[ !PrimeQ[trnglr - 1] && !PrimeQ[trnglr + 1], k++ ]; k]; Array[f, 105]