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A224934 Primes p for which there exists no prime q, different from p, such that p+q-1 is the next prime after p.

%I A224934 #12 Nov 22 2016 03:10:49
%S A224934 2,3,89,113,293,317,359,389,401,449,479,491,683,701,719,743,761,773,
%T A224934 839,863,887,911,929,953,983,1109,1163,1193,1327,1373,1409,1439,1523,
%U A224934 1559,1571,1583,1637,1669,1733,1823,1847,1979,2003,2039,2153,2179,2213,2243
%N A224934 Primes p for which there exists no prime q, different from p, such that p+q-1 is the next prime after p.
%C A224934 If we relax the restriction on q, where q is different from p, 2 and 3 fail to be members of this sequence.
%C A224934 Primes p = prime(k) for which A076368(k+1) = p or A076368(k+1) is composite. - _Robert Israel_, Nov 21 2016
%H A224934 Robert Israel, <a href="/A224934/b224934.txt">Table of n, a(n) for n = 1..10000</a>
%e A224934 89 is in the list because there exists no prime q such that 89 + q - 1 = 97.
%p A224934 N:= 10^4: # to get all terms p for which the next prime <= N
%p A224934 P:= select(isprime, [2,seq(i,i=3..N,2)]):
%p A224934 G:= P[2..-1]-P[1..-2]:
%p A224934 P[select(t -> G[t]=P[t]-1 or not isprime(G[t]+1), [$1..nops(G)])]; # _Robert Israel_, Nov 21 2016
%t A224934 t = {}; Do[p = Prime[n]; If[FreeQ[Table[k = p + Prime[i] - 1, {i, n - 1}], Prime[n + 1]], AppendTo[t, p]], {n, 335}]; t
%Y A224934 Cf. A076368, A224748.
%K A224934 nonn
%O A224934 1,1
%A A224934 _Jayanta Basu_, Apr 20 2013