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A234644 Primes p with q(p) - 1 also prime, where q(.) is the strict partition function (A000009). 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 18:20 EDT 2019. Contains 322283 sequences. (Running on oeis4.)