A113155 - OEIS

%I #9 Nov 21 2013 12:48:45

%S 311,401,863,907,1117,1213,1237,1399,1427,2333,3299,3533,3821,3967,

%T 4243,4493,5273,5779,6199,6521,7069,8219,8369,8623,8741,8837,8929,

%U 9277,9613,10139,10601,10631,10939,11621,11779,12197,12241,12343,12401,12457

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

%C 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 Harvey P. Dale, <a href="/A113155/b113155.txt">Table of n, a(n) for n = 1..1000</a>

%F 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 a(1) = 311 since prevprime(311) + nextprime(311) = 307 + 313 = 620 = 31 * 20.

%e a(2) = 401 since prevprime(401) + nextprime(401) = 397 + 409 = 806 = 31 * 26.

%e a(3) = 863 since prevprime(863) + nextprime(863) = 859 + 877 = 1736 = 31 * 56.

%e a(4) = 907 since prevprime(907) + nextprime(907) = 887 + 911 = 1798 = 31 * 58.

%t Prime@Select[Range[2, 1531], Mod[Prime[ # - 1] + Prime[ # + 1], 31] == 0 &] (* _Robert G. Wilson v_ *)

%t Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[#[[1]]+#[[3]], 31]&]][[2]] (* _Harvey P. Dale_, Mar 23 2012 *)

%Y Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 05 2006

%E Corrected and extended by _Robert G. Wilson v_, Jan 11 2006