

A234569


Primes p with P(p1) also prime, where P(.) is the partition function (A000041).


12



3, 5, 7, 37, 367, 499, 547, 659, 1087, 1297, 1579, 2137, 2503, 3169, 3343, 4457, 4663, 5003, 7459, 9293, 16249, 23203, 34667, 39971, 41381, 56383, 61751, 62987, 72661, 77213, 79697, 98893, 101771, 127081, 136193, 188843, 193811, 259627, 267187, 282913, 315467, 320563, 345923, 354833, 459029, 482837, 496477, 548039, 641419, 647189
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OFFSET

1,1


COMMENTS

By the conjecture in A234567, this sequence should have infinitely many terms. It seems that a(n+1) < a(n) + a(n1) for all n > 5.
The bfile lists all terms not exceeding the 500000th prime 7368787. Note that P(a(113)1) is a prime having 2999 decimal digits.
See also A234572 for primes of the form P(p1) with p prime.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..113
Z.W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014


EXAMPLE

a(1) = 3 since P(21) = 1 is not prime, but P(31) = 2 is prime.
a(2) = 5 since P(51) = 5 is prime.
a(3) = 7 since P(71) = 11 is prime.


MATHEMATICA

n=0; Do[If[PrimeQ[PartitionsP[Prime[k]1]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10^6}]


CROSSREFS

Cf. A000040, A000041, A049575, A233346, A234470, A234475, A234514, A234530, A234567, A234572, A234615, A234644
Sequence in context: A126359 A182373 A087363 * A037287 A163797 A130536
Adjacent sequences: A234566 A234567 A234568 * A234570 A234571 A234572


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Dec 28 2013


STATUS

approved



