A112795 Primes such that the sum of the predecessor and successor primes is divisible by 13.

79, 103, 139, 233, 271, 389, 401, 457, 587, 619, 641, 769, 883, 967, 1013, 1031, 1153, 1213, 1249, 1289, 1301, 1429, 1523, 1559, 1571, 1699, 1721, 1789, 1847, 1901, 2039, 2089, 2111, 2273, 2297, 2459, 2579, 2593, 2663, 3359, 3371, 3373, 3449, 3491, 3527

Offset

1,1

Comments

There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.

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 13. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 13.

Example

a(1) = 79 because prevprime(79) + nextprime(79) = 73 + 83 = 156 = 13 * 12.
a(2) = 103 because prevprime(103) + nextprime(103) = 101 + 107 = 208 = 13 * 16.
a(3) = 139 because prevprime(139) + nextprime(139) = 137 + 149 = 286 = 13 * 22.
a(4) = 233 because prevprime(233) + nextprime(233) = 229 + 239 = 468 = 13 * 36.

Mathematica

Prime@ Select[Range[2, 496], Mod[Prime[ # - 1] + Prime[ # + 1], 13] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[500]], 3, 1], Divisible[#[[1]]+#[[3]], 13]&] [[All, 2]] (* Harvey P. Dale, Apr 06 2022 *)

Crossrefs

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

Sequence in context: A193142 A033250 A139922 * A107162 A238186 A135143

Adjacent sequences: A112792 A112793 A112794 * A112796 A112797 A112798

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 01 2006

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

Status

approved