A112795 - OEIS

%I #13 Apr 06 2022 11:12:38

%S 79,103,139,233,271,389,401,457,587,619,641,769,883,967,1013,1031,

%T 1153,1213,1249,1289,1301,1429,1523,1559,1571,1699,1721,1789,1847,

%U 1901,2039,2089,2111,2273,2297,2459,2579,2593,2663,3359,3371,3373,3449,3491,3527

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

%C 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 Harvey P. Dale, <a href="/A112795/b112795.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 13. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 13.

%e a(1) = 79 because prevprime(79) + nextprime(79) = 73 + 83 = 156 = 13 * 12.

%e a(2) = 103 because prevprime(103) + nextprime(103) = 101 + 107 = 208 = 13 * 16.

%e a(3) = 139 because prevprime(139) + nextprime(139) = 137 + 149 = 286 = 13 * 22.

%e a(4) = 233 because prevprime(233) + nextprime(233) = 229 + 239 = 468 = 13 * 36.

%t Prime@ Select[Range[2, 496], Mod[Prime[ # - 1] + Prime[ # + 1], 13] == 0 &] (* _Robert G. Wilson v_ *)

%t Select[Partition[Prime[Range[500]],3,1],Divisible[#[[1]]+#[[3]],13]&] [[All,2]] (* _Harvey P. Dale_, Apr 06 2022 *)

%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 01 2006

%E More terms from _Robert G. Wilson v_, Jan 05 2006