A113155 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

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

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.

EXAMPLE

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.

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 *)

CROSSREFS