This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112847 #15 Jul 22 2019 19:47:38 %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, %U A112847 4903,5039,5309,5431,5867,5881,6091,6211,6277,6673,6781,6803,7309,7499,8147 %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. A112789 is analogous to this, but mod 11. %H A112847 Harvey P. Dale, <a href="/A112847/b112847.txt">Table of n, a(n) for n = 1..1000</a> %F A112847 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 23. %F A112847 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_, Jan 05 2006 *) %t A112847 Select[Partition[Prime[Range[1100]],3,1],Divisible[#[[1]]+#[[3]],23]&][[All,2]] (* _Harvey P. Dale_, Jul 22 2019 *) %Y A112847 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158. %K A112847 easy,nonn %O A112847 1,1 %A A112847 _Jonathan Vos Post_, Jan 01 2006 %E A112847 More terms from _Robert G. Wilson v_, Jan 05 2006