A113155 Primes such that the sum of the predecessor and successor primes is divisible by 31.

311, 401, 863, 907, 1117, 1213, 1237, 1399, 1427, 2333, 3299, 3533, 3821, 3967, 4243, 4493, 5273, 5779, 6199, 6521, 7069, 8219, 8369, 8623, 8741, 8837, 8929, 9277, 9613, 10139, 10601, 10631, 10939, 11621, 11779, 12197, 12241, 12343, 12401, 12457

Offset: 1

Author

Jonathan Vos Post, Jan 05 2006

Keywords

• easy
• nonn

Comments

A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.

Examples

			a(1) = 311 since prevprime(311) + nextprime(311) = 307 + 313 = 620 = 31 * 20.
a(2) = 401 since prevprime(401) + nextprime(401) = 397 + 409 = 806 = 31 * 26.
a(3) = 863 since prevprime(863) + nextprime(863) = 859 + 877 = 1736 = 31 * 56.
a(4) = 907 since prevprime(907) + nextprime(907) = 887 + 911 = 1798 = 31 * 58.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

Mathematica

Prime@Select[Range[2, 1531], Mod[Prime[ # - 1] + Prime[ # + 1], 31] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[#[[1]]+#[[3]], 31]&]][[2]] (* Harvey P. Dale, Mar 23 2012 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 31. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 31.

Extensions

Corrected and extended by Robert G. Wilson v, Jan 11 2006