A112847 - OEIS

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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

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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 *)