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

1,1

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.

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A141246 A288445 A087759 * A299791 A230359 A161548

Adjacent sequences: A234641 A234642 A234643 * A234645 A234646 A234647

Keyword

nonn

Author

Zhi-Wei Sun, Dec 29 2013

Status

approved