A275697 - OEIS

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

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OFFSET

1,1

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

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])];