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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
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
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved