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A112796 Primes such that the sum of the predecessor and successor primes is divisible by 17.

%I A112796 #13 Oct 06 2020 19:48:55
%S A112796 151,191,199,421,491,613,829,883,937,1409,1447,1459,1667,1693,1871,
%T A112796 2027,2203,2347,2381,2503,2687,2857,2957,3041,3121,3259,3517,3557,
%U A112796 3571,3583,3847,3929,4153,4271,4591,4793,4999,5011,5051,5273,5323,5407,5441,5449
%N A112796 Primes such that the sum of the predecessor and successor primes is divisible by 17.
%C A112796 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 A112796 Harvey P. Dale, <a href="/A112796/b112796.txt">Table of n, a(n) for n = 1..1000</a>
%F A112796 a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 17. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 17.
%e A112796 a(1) = 151 because prevprime(151) + nextprime(151) = 149 + 157 = 306 = 17 * 8.
%e A112796 a(2) = 191 because prevprime(191) + nextprime(191) = 181 + 193 = 374 = 17 * 22.
%e A112796 a(3) = 199 because prevprime(199) + nextprime(199) = 197 + 211 = 408 = 17 * 24.
%e A112796 a(4) = 421 because prevprime(421) + nextprime(421) = 419 + 431 = 850 = 17 * 50.
%t A112796 Prime@ Select[Range[2, 731], Mod[Prime[ # - 1] + Prime[ # + 1], 17] == 0 &] (* _Robert G. Wilson v_ *)
%t A112796 Select[Partition[Prime[Range[800]],3,1],Divisible[#[[1]]+#[[3]],17]&][[All,2]] (* _Harvey P. Dale_, Oct 06 2020 *)
%Y A112796 Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
%K A112796 easy,nonn
%O A112796 1,1
%A A112796 _Jonathan Vos Post_, Jan 01 2006
%E A112796 More terms from _Robert G. Wilson v_, Jan 05 2006