A112681 Primes such that the sum of the predecessor and successor primes is divisible by 3.

23, 29, 31, 37, 47, 59, 61, 67, 73, 79, 83, 89, 131, 137, 151, 163, 167, 179, 199, 223, 233, 239, 251, 269, 271, 277, 331, 337, 353, 359, 367, 379, 383, 389, 433, 439, 443, 449, 467, 479, 503, 521, 523, 547, 557, 569, 571, 577, 587, 599, 601, 613, 619, 631

Offset: 1

Author

Carlos Alves, Dec 30 2005

Keywords

• easy
• nonn

Examples

			23 is in the sequence because 19+29=48 and 3|48.
29 is in the sequence because 29+31=60 and 3|60.
		

Links

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

Crossrefs

Analogs where 3 is replaced by other primes:

Divisor: ..3 .......5 .......7 ......11 ......13 ......17 ......19 ......23 ......29 ......31 ......37 ......41 ......43

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

Programs

Mathematica

Prime@Select[Range[2, 117], Mod[Prime[ # - 1] + Prime[ # + 1], 3] == 0 &] (* Robert G. Wilson v, Jan 11 2006 *)
Select[Partition[Prime[Range[150]],3,1],Divisible[#[[1]]+#[[3]],3]&][[All,2]] (* Harvey P. Dale, Aug 18 2020 *)