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 A112804 #7 Oct 31 2013 12:17:34 %S A112804 59,97,683,797,821,1049,1307,1579,1709,1787,1913,2029,2143,2161,2281, %T A112804 2339,2393,2437,2557,2659,2791,2851,2887,3389,3413,3533,3557,3643, %U A112804 3779,3853,4177,4241,4447,4507,4583,4957,4973,5119,5641,5813,6043,6133,7069 %N A112804 Primes such that the sum of the predecessor and successor primes is divisible by 19. %C A112804 There is a trivial analog for every prime >= 3. A112681 is analogous mod 3. A112731 is analogous mod 7. A112789 is analogous mod 11. %F A112804 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 19. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 19. %e A112804 a(1) = 59 because prevprime(59) + nextprime(59) = 53 + 61 = 114 = 19 * 6. %e A112804 a(2) = 97 because prevprime(97) + nextprime(97) = 89 + 101 = 190 = 19 * 10. %e A112804 a(3) = 683 because prevprime(683) + nextprime(683) = 677 + 691 = 1368 = 19 * 72. %e A112804 a(4) = 797 because prevprime(797) + nextprime(797) = 787 + 809 = 1596 = 19 * 84. %t A112804 Prime@ Select[Range[2, 912], Mod[Prime[ # - 1] + Prime[ # + 1], 19] == 0 &] (* _Robert G. Wilson v_ *) %Y A112804 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158. %K A112804 easy,nonn %O A112804 1,1 %A A112804 _Jonathan Vos Post_, Jan 01 2006 %E A112804 More terms from _Robert G. Wilson v_, Jan 05 2006