Search: id:A112847
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%I A112847
%S A112847 229,277,317,461,643,919,1033,1307,1427,1609,1777,1789,2089,2207,2347,
%T A112847 2531,2551,2647,2969,3121,3169,3517,3659,3701,3727,4211,4421,4549,4903,
%U A112847 5039,5309,5431,5867,5881,6091,6211,6277,6673,6781,6803,7309,7499,8147
%N A112847 Primes such that the sum of the predecessor and successor primes is divisible 
               by 23.
%C A112847 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.
%F A112847 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.
%e A112847 a(1) = 229 because prevprime(229) + nextprime(229) = 227 + 433 = 460 
               = 23 * 20.
%e A112847 a(2) = 277 because prevprime(277) + nextprime(277) = 271 + 281 = 552 
               = 23 * 24.
%e A112847 a(3) = 317 because prevprime(317) + nextprime(317) = 313 + 331 = 644 
               = 23 * 28.
%e A112847 a(4) = 461 because prevprime(461) + nextprime(461) = 457 + 463 = 920 
               = 23 * 40.
%t A112847 Prime@ Select[Range[2, 1032], Mod[Prime[ # - 1] + Prime[ # + 1], 23] 
               == 0 &] (* Robert G. Wilson v *)
%Y A112847 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, 
               A112847, A112859, A113155, A113156, A113157, A113158.
%Y A112847 Sequence in context: A119711 A062589 A094612 this_sequence A157348 A142221 
               A142779
%Y A112847 Adjacent sequences: A112844 A112845 A112846 this_sequence A112848 A112849 
               A112850
%K A112847 easy,nonn
%O A112847 1,1
%A A112847 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 01 2006
%E A112847 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 05 2006

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