A234644 Primes p with q(p) - 1 also prime, where q(.) is the strict partition function (A000009).

5, 11, 13, 17, 19, 23, 41, 43, 53, 59, 79, 103, 151, 191, 269, 277, 283, 373, 419, 521, 571, 577, 607, 829, 859, 1039, 2503, 2657, 2819, 3533, 3671, 4079, 4153, 4243, 4517, 4951, 4987, 5689, 5737, 5783, 7723, 8101, 9137, 9173, 9241, 9539, 11467, 12323, 12697, 15017, 15277, 15427, 15803, 16057, 17959, 18661

Offset: 1

Author

Zhi-Wei Sun, Dec 29 2013

Keywords

• nonn

Comments

By the conjecture in A234615, this sequence should have infinitely many terms.

See A234647 for primes of the form q(p) - 1 with p prime.

See also A234530 for a similar sequence.

Examples

			a(1) = 5 since neither q(2) - 1 = 0 nor q(3) - 1 = 1 is prime, but q(5) - 1 = 2 is prime.
a(2) = 11 since q(7) - 1 = 4 is composite, but q(11) - 1 = 11 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..140
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

Cf. A000009, A000040, A234470, A234475, A234514, A234530, A234567, A234569, A234572, A234615, A234647.

Programs

Mathematica

q[k_]:=q[k]=PrimeQ[PartitionsQ[Prime[k]]-1]
n=0;Do[If[q[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10^5}]