cp's OEIS Frontend

A113155 Primes such that the sum of the predecessor and successor primes is divisible by 31.

%I A113155 #9 Nov 21 2013 12:48:45
%S A113155 311,401,863,907,1117,1213,1237,1399,1427,2333,3299,3533,3821,3967,
%T A113155 4243,4493,5273,5779,6199,6521,7069,8219,8369,8623,8741,8837,8929,
%U A113155 9277,9613,10139,10601,10631,10939,11621,11779,12197,12241,12343,12401,12457
%N A113155 Primes such that the sum of the predecessor and successor primes is divisible by 31.
%C A113155 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 A113155 Harvey P. Dale, <a href="/A113155/b113155.txt">Table of n, a(n) for n = 1..1000</a>
%F A113155 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 31. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 31.
%e A113155 a(1) = 311 since prevprime(311) + nextprime(311) = 307 + 313 = 620 = 31 * 20.
%e A113155 a(2) = 401 since prevprime(401) + nextprime(401) = 397 + 409 = 806 = 31 * 26.
%e A113155 a(3) = 863 since prevprime(863) + nextprime(863) = 859 + 877 = 1736 = 31 * 56.
%e A113155 a(4) = 907 since prevprime(907) + nextprime(907) = 887 + 911 = 1798 = 31 * 58.
%t A113155 Prime@Select[Range[2, 1531], Mod[Prime[ # - 1] + Prime[ # + 1], 31] == 0 &] (* _Robert G. Wilson v_ *)
%t A113155 Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[#[[1]]+#[[3]], 31]&]][[2]] (* _Harvey P. Dale_, Mar 23 2012 *)
%Y A113155 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
%K A113155 easy,nonn
%O A113155 1,1
%A A113155 _Jonathan Vos Post_, Jan 05 2006
%E A113155 Corrected and extended by _Robert G. Wilson v_, Jan 11 2006