

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
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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

ZhiWei 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

ZhiWei Sun, Dec 29 2013


STATUS

approved



