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

Author

Jonathan Vos Post, Jan 01 2006

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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.

Extensions

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