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