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

1,1

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.

Links

Table of n, a(n) for n=1..53.

Example

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

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]]

Crossrefs

Cf. Complement of A125771.

Sequence in context: A308711 A024785 A069866 * A233282 A001000 A094947

Adjacent sequences: A125769 A125770 A125771 * A125773 A125774 A125775

Keyword

nonn

Author

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

Status

approved