

A234530


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


14



2, 3, 11, 13, 29, 37, 47, 71, 79, 89, 103, 127, 131, 179, 181, 197, 233, 271, 331, 379, 499, 677, 691, 757, 887, 911, 1019, 1063, 1123, 1279, 1429, 1531, 1559, 1637, 2251, 2719, 3571, 4007, 4201, 4211, 4297, 4447, 4651, 4967, 5953, 6131, 7937, 8233, 8599, 8819, 9013, 11003, 11093, 11813, 12251, 12889, 12953, 13487, 13687, 15259
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OFFSET

1,1


COMMENTS

By the conjecture in A234514, this sequence should have infinitely many terms.
It seems that a(n+1) < a(n) + a(n1) for all n > 4.
See A234366 for primes of the form q(p) + 1 with p prime.
See also A234644 for a similar sequence.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..150


EXAMPLE

a(1) = 2 since 2 and q(2) + 1 = 2 are both prime.
a(2) = 3 since 3 and q(3) + 1 = 3 are both prime.
a(3) = 11 since 11 and q(11) + 1 = 13 are both prime.


MATHEMATICA

n=0; Do[If[PrimeQ[PartitionsQ[Prime[k]]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10^5}]
Select[Prime[Range[2000]], PrimeQ[PartitionsQ[#]+1]&] (* Harvey P. Dale, Apr 23 2017 *)


CROSSREFS

Cf. A000009, A000040, A233346, A233393, A234366, A234470, A234475, A234514, A234567, A234569, A234572, A234615, A234644, A234647
Sequence in context: A215378 A078763 A157884 * A235632 A085306 A161322
Adjacent sequences: A234527 A234528 A234529 * A234531 A234532 A234533


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Dec 27 2013


STATUS

approved



