A162565 Those primes p such that (p-q) divides (p-1), where q is the greatest prime < p.

3, 5, 7, 13, 17, 19, 31, 37, 41, 43, 61, 67, 73, 79, 97, 101, 103, 109, 113, 127, 139, 151, 157, 163, 181, 191, 193, 197, 199, 229, 233, 241, 251, 271, 277, 281, 283, 313, 317, 337, 349, 353, 373, 379, 401, 409, 421, 431, 433, 439, 457, 461, 463, 523, 541, 547

Offset: 1

Author

Leroy Quet, Jul 06 2009

Keywords

• nonn

Comments

A006512 (greater of twin primes) is a subsequence. - Michel Marcus, Feb 27 2019

Except for 11, A090609 is a subsequence. - Davide Rotondo, Feb 12 2025

Examples

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

Links

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

Crossrefs

Cf. A006512, A162566.

Programs

Maple

A162565 := proc(n) local p,q; p := ithprime(n) ; q := prevprime(p) ; if (p-1) mod (p-q) = 0 then printf("%d,",p); fi; end: seq(A162565(n),n=2..200) ; # R. J. Mathar, Jul 13 2009

Mathematica

Transpose[Select[Partition[Prime[Range[110]],2,1],Divisible[#[[2]]-1, #[[2]] - #[[1]]]&]][[2]] (* Harvey P. Dale, Mar 18 2016 *)

PARI

isok(p) = isprime(p) && !((p-1) % (p-precprime(p-1))); \\ Michel Marcus, Feb 12 2025

Extensions

More primes from R. J. Mathar, Jul 13 2009