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A112795 Primes such that the sum of the predecessor and successor primes is divisible by 13.

%I A112795 #13 Apr 06 2022 11:12:38
%S A112795 79,103,139,233,271,389,401,457,587,619,641,769,883,967,1013,1031,
%T A112795 1153,1213,1249,1289,1301,1429,1523,1559,1571,1699,1721,1789,1847,
%U A112795 1901,2039,2089,2111,2273,2297,2459,2579,2593,2663,3359,3371,3373,3449,3491,3527
%N A112795 Primes such that the sum of the predecessor and successor primes is divisible by 13.
%C A112795 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 A112795 Harvey P. Dale, <a href="/A112795/b112795.txt">Table of n, a(n) for n = 1..1000</a>
%F A112795 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 13. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 13.
%e A112795 a(1) = 79 because prevprime(79) + nextprime(79) = 73 + 83 = 156 = 13 * 12.
%e A112795 a(2) = 103 because prevprime(103) + nextprime(103) = 101 + 107 = 208 = 13 * 16.
%e A112795 a(3) = 139 because prevprime(139) + nextprime(139) = 137 + 149 = 286 = 13 * 22.
%e A112795 a(4) = 233 because prevprime(233) + nextprime(233) = 229 + 239 = 468 = 13 * 36.
%t A112795 Prime@ Select[Range[2, 496], Mod[Prime[ # - 1] + Prime[ # + 1], 13] == 0 &] (* _Robert G. Wilson v_ *)
%t A112795 Select[Partition[Prime[Range[500]],3,1],Divisible[#[[1]]+#[[3]],13]&] [[All,2]] (* _Harvey P. Dale_, Apr 06 2022 *)
%Y A112795 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
%K A112795 easy,nonn
%O A112795 1,1
%A A112795 _Jonathan Vos Post_, Jan 01 2006
%E A112795 More terms from _Robert G. Wilson v_, Jan 05 2006