A162566 Those primes p where (q-p) divides (p+1), where q is the least prime > p.

2, 3, 5, 7, 11, 17, 19, 23, 29, 41, 43, 47, 53, 59, 67, 71, 79, 83, 101, 103, 107, 127, 131, 137, 139, 149, 163, 167, 173, 179, 191, 197, 223, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 347, 353, 359, 379, 383, 409, 419, 431, 439, 443, 461, 463, 467

Offset: 1

Author

Leroy Quet, Jul 06 2009

Keywords

• nonn

Examples

			The 17th prime is 59 and the 18th prime is 61. (61-59) = 2, and 2 divides 59+1 = 60. So 59 is in the sequence.
		

Links

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

Crossrefs

Cf. A162565.

Programs

Mathematica

For[n = 1, n <= 1000, n++, If[Mod[Prime[n] + 1, Prime[n + 1] - Prime[n]] == 0, Print[Prime[n]]]] (* Jasper Mulder (jasper.mulder(AT)planet.nl), Jul 15 2009 *)
Select[Partition[Prime[Range[100]],2,1],Divisible[#[[1]]+1,#[[2]]-#[[1]]]&][[;;,1]] (* Harvey P. Dale, Aug 06 2023 *)

Extensions

More terms from Jasper Mulder (jasper.mulder(AT)planet.nl), Jul 15 2009