A113156 Primes such that the sum of the predecessor and successor primes is divisible by 37.

181, 443, 557, 661, 967, 1109, 1553, 1951, 2069, 2441, 2551, 3257, 3371, 4001, 4783, 5179, 5987, 6143, 6217, 6473, 6701, 6803, 6841, 7213, 8431, 8663, 8839, 8887, 9283, 9511, 9839, 9883, 10177, 10589, 10771, 10883, 11059, 11093, 11173, 11437, 11657

Offset: 1

Author

Jonathan Vos Post, Jan 05 2006

Keywords

• easy
• nonn

Comments

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.

Examples

			a(1) = 181 since prevprime(181) + nextprime(181) = 179 + 191 = 370 = 37 * 10.
a(2) = 443 since prevprime(443) + nextprime(443) = 439 + 449 = 888 = 37 * 24.
a(3) = 557 since prevprime(557) + nextprime(557) = 547 + 563 = 1110 = 37 * 30.
a(4) = 661 since prevprime(661) + nextprime(661) = 659 + 673 = 1332 = 37 * 36.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

Prime@Select[Range[2, 1463], Mod[Prime[ # - 1] + Prime[ # + 1], 37] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[First[#]+ Last[#],37]&]][[2]] (* Harvey P. Dale, Dec 19 2011 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 37. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 37.

Extensions

More terms from Robert G. Wilson v, Jan 11 2006