A275697 Primes p such that gcd(p-1, q-1) = q - p, where q is the next prime after p.

2, 3, 5, 11, 13, 17, 29, 31, 37, 41, 59, 61, 71, 73, 89, 97, 101, 107, 109, 113, 137, 149, 151, 157, 179, 181, 191, 193, 197, 227, 229, 239, 241, 269, 271, 277, 281, 311, 313, 331, 347, 349, 367, 373, 397, 401, 419, 421, 431, 433, 449, 457, 461, 521, 523

Offset: 1

Author

Thomas Ordowski and Robert Israel, Aug 05 2016

Keywords

• nonn

Comments

Primes prime(k) such that prime(k) == 1 (mod A001223(k)).

Problem: are there infinitely many such primes?

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001223.

Contains A001359.

Except for 2, contained in A090190.

Programs

Maple

N:= 1000: # to get all terms <= N
P:= select(isprime, [2,seq(i,i=3..nextprime(N),2)]):
P[select(i -> (P[i] - 1) mod (P[i+1]-P[i]) = 0, [$1..nops(P)-1])];

Mathematica

Select[Partition[Prime[Range[100]],2,1],GCD[#[[1]]-1,#[[2]]-1] == #[[2]]- #[[1]]&][[All,1]] (* Harvey P. Dale, Apr 18 2018 *)

PARI

is(n) = ispseudoprime(n) && gcd(n-1, nextprime(n+1)-1)==nextprime(n+1)-n \\ Felix Fröhlich, Aug 06 2016