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A113156 Primes such that the sum of the predecessor and successor primes is divisible by 37.

%I A113156 #15 Feb 07 2015 12:32:28
%S A113156 181,443,557,661,967,1109,1553,1951,2069,2441,2551,3257,3371,4001,
%T A113156 4783,5179,5987,6143,6217,6473,6701,6803,6841,7213,8431,8663,8839,
%U A113156 8887,9283,9511,9839,9883,10177,10589,10771,10883,11059,11093,11173,11437,11657
%N A113156 Primes such that the sum of the predecessor and successor primes is divisible by 37.
%C A113156 A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.
%H A113156 Harvey P. Dale, <a href="/A113156/b113156.txt">Table of n, a(n) for n = 1..1000</a>
%F A113156 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 37. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 37.
%e A113156 a(1) = 181 since prevprime(181) + nextprime(181) = 179 + 191 = 370 = 37 * 10.
%e A113156 a(2) = 443 since prevprime(443) + nextprime(443) = 439 + 449 = 888 = 37 * 24.
%e A113156 a(3) = 557 since prevprime(557) + nextprime(557) = 547 + 563 = 1110 = 37 * 30.
%e A113156 a(4) = 661 since prevprime(661) + nextprime(661) = 659 + 673 = 1332 = 37 * 36.
%t A113156 Prime@Select[Range[2, 1463], Mod[Prime[ # - 1] + Prime[ # + 1], 37] == 0 &] (* _Robert G. Wilson v_ *)
%t A113156 Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[First[#]+ Last[#],37]&]][[2]] (* _Harvey P. Dale_, Dec 19 2011 *)
%Y A113156 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
%K A113156 easy,nonn
%O A113156 1,1
%A A113156 _Jonathan Vos Post_, Jan 05 2006
%E A113156 More terms from _Robert G. Wilson v_, Jan 11 2006