A112847 Primes such that the sum of the predecessor and successor primes is divisible by 23.

229, 277, 317, 461, 643, 919, 1033, 1307, 1427, 1609, 1777, 1789, 2089, 2207, 2347, 2531, 2551, 2647, 2969, 3121, 3169, 3517, 3659, 3701, 3727, 4211, 4421, 4549, 4903, 5039, 5309, 5431, 5867, 5881, 6091, 6211, 6277, 6673, 6781, 6803, 7309, 7499, 8147

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 23.

a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 23.

Example

a(1) = 229 because prevprime(229) + nextprime(229) = 227 + 433 = 460 = 23 * 20.
a(2) = 277 because prevprime(277) + nextprime(277) = 271 + 281 = 552 = 23 * 24.
a(3) = 317 because prevprime(317) + nextprime(317) = 313 + 331 = 644 = 23 * 28.
a(4) = 461 because prevprime(461) + nextprime(461) = 457 + 463 = 920 = 23 * 40.

Mathematica

Prime@ Select[Range[2, 1032], Mod[Prime[ # - 1] + Prime[ # + 1], 23] == 0 &] (* Robert G. Wilson v, Jan 05 2006 *)
Select[Partition[Prime[Range[1100]], 3, 1], Divisible[#[[1]]+#[[3]], 23]&][[All, 2]] (* Harvey P. Dale, Jul 22 2019 *)

Crossrefs

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

Sequence in context: A094612 A250237 A350165 * A157348 A142221 A142779

Adjacent sequences: A112844 A112845 A112846 * A112848 A112849 A112850

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 01 2006

Extensions

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

Status

approved