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

2, 3, 89, 113, 293, 317, 359, 389, 401, 449, 479, 491, 683, 701, 719, 743, 761, 773, 839, 863, 887, 911, 929, 953, 983, 1109, 1163, 1193, 1327, 1373, 1409, 1439, 1523, 1559, 1571, 1583, 1637, 1669, 1733, 1823, 1847, 1979, 2003, 2039, 2153, 2179, 2213, 2243

Offset: 1

Author

Jayanta Basu, Apr 20 2013

Keywords

• nonn

Comments

If we relax the restriction on q, where q is different from p, 2 and 3 fail to be members of this sequence.

Primes p = prime(k) for which A076368(k+1) = p or A076368(k+1) is composite. - Robert Israel, Nov 21 2016

Examples

			89 is in the list because there exists no prime q such that 89 + q - 1 = 97.
		

Links

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

Crossrefs

Cf. A076368, A224748.

Programs

Maple

N:= 10^4: # to get all terms p for which the next prime <= N
P:= select(isprime, [2,seq(i,i=3..N,2)]):
G:= P[2..-1]-P[1..-2]:
P[select(t -> G[t]=P[t]-1 or not isprime(G[t]+1), [$1..nops(G)])]; # Robert Israel, Nov 21 2016

Mathematica

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