A125772 Primes not of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 9.

2, 3, 5, 7, 13, 17, 23, 47, 53, 97, 103, 163, 173, 193, 227, 257, 283, 317, 347, 353, 367, 373, 383, 443, 457, 487, 523, 557, 563, 607, 653, 677, 733, 743, 773, 787, 823, 853, 877, 887, 907, 977, 983, 997, 1033, 1097, 1163, 1193, 1213, 1237, 1277, 1283, 1307

Offset: 1

Author

Jonathan Vos Post & Robert G. Wilson v, Dec 05 2006

Keywords

• nonn

Comments

Since all primes would eventually appear in A125765 or A125766 because (p +/-1) times 1(1+1)/2 equals (p +/- 1) let us not use the first triangular number 1.

Examples

			17 is not of the form j*T_k +/- 1 for any j = 1 or 2 and the triangular numbers, 10, 15 or 21.
		

Crossrefs

Cf. Complement of A125771.

Programs

Mathematica

s = {}; Do[m = j*k*(k + 1)/2; If[PrimeQ[m - 1], AppendTo[s, m - 1]]; If[PrimeQ[m + 1], AppendTo[s, m + 1]], {j, 140}, {k, 4, 43}]; Complement[ Prime@ Range@220, Take[Union@s, 200]]