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 A112847 Primes such that the sum of the predecessor and successor primes is divisible by 23. 15
 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 (list; graph; refs; listen; history; text; internal format)
 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], 3, 1], Divisible[#[]+#[], 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: A250236 A094612 A250237 * 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

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)