cp's OEIS Frontend

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

%I A275697 #17 Aug 01 2019 04:09:18
%S A275697 2,3,5,11,13,17,29,31,37,41,59,61,71,73,89,97,101,107,109,113,137,149,
%T A275697 151,157,179,181,191,193,197,227,229,239,241,269,271,277,281,311,313,
%U A275697 331,347,349,367,373,397,401,419,421,431,433,449,457,461,521,523
%N A275697 Primes p such that gcd(p-1, q-1) = q - p, where q is the next prime after p.
%C A275697 Primes prime(k) such that prime(k) == 1 (mod A001223(k)).
%C A275697 Problem: are there infinitely many such primes?
%H A275697 Robert Israel, <a href="/A275697/b275697.txt">Table of n, a(n) for n = 1..10000</a>
%p A275697 N:= 1000: # to get all terms <= N
%p A275697 P:= select(isprime, [2,seq(i,i=3..nextprime(N),2)]):
%p A275697 P[select(i -> (P[i] - 1) mod (P[i+1]-P[i]) = 0, [$1..nops(P)-1])];
%t A275697 Select[Partition[Prime[Range[100]],2,1],GCD[#[[1]]-1,#[[2]]-1] == #[[2]]- #[[1]]&][[All,1]] (* _Harvey P. Dale_, Apr 18 2018 *)
%o A275697 (PARI) is(n) = ispseudoprime(n) && gcd(n-1, nextprime(n+1)-1)==nextprime(n+1)-n \\ _Felix Fröhlich_, Aug 06 2016
%Y A275697 Cf. A000040, A001223.
%Y A275697 Contains A001359.
%Y A275697 Except for 2, contained in A090190.
%K A275697 nonn
%O A275697 1,1
%A A275697 _Thomas Ordowski_ and _Robert Israel_, Aug 05 2016