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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. A112xxx is analogous to this, but mod 11.

LINKS

Table of n, a(n) for n=1..43.

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 *)

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 December 18 19:05 EST 2014. Contains 252174 sequences.