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

1,1

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.

Links

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

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A108847 A063360 A217499 * A142391 A142552 A211553

Adjacent sequences: A113153 A113154 A113155 * A113157 A113158 A113159

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 05 2006

Extensions

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

Status

approved