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

Author

Jonathan Vos Post, Jan 01 2006

Keywords

• easy
• nonn

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.

Examples

			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.
		

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, 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 *)

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.

Extensions

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