A112794 Primes such that the sum of the predecessor and successor primes is divisible by 5.

5, 11, 19, 41, 71, 73, 89, 97, 101, 109, 137, 149, 181, 229, 241, 281, 293, 311, 349, 359, 389, 397, 409, 419, 421, 433, 449, 457, 461, 487, 541, 557, 587, 631, 701, 709, 743, 751, 787, 811, 859, 881, 887, 919, 937, 991, 997, 1009, 1021, 1033, 1049, 1051, 1063

Offset

1,1

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 5. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 5.

Example

a(1) = 5 because prevprime(5) + nextprime(5) = 3 + 7 = 10 = 5 * 2.
a(2) = 11 because prevprime(11) + nextprime(11) = 7 + 13 = 20 = 5 * 4.
a(3) = 19 because prevprime(19) + nextprime(19) = 17 + 23 = 40 = 5 * 8.
a(4) = 41 because prevprime(41) + nextprime(41) = 37 + 43 = 80 = 5 * 16.

Mathematica

Prime@ Select[Range[2, 179], Mod[Prime[ # - 1] + Prime[ # + 1], 5] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[200]], 3, 1], Divisible[#[[1]]+#[[3]], 5]&] [[All, 2]] (* Harvey P. Dale, May 18 2019 *)

Crossrefs

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

Sequence in context: A105914 A289530 A106016 * A163419 A375316 A371668

Adjacent sequences: A112791 A112792 A112793 * A112795 A112796 A112797

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 01 2006

Extensions

Corrected and extended by Robert G. Wilson v, Jan 05 2006

Status

approved