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A234569 Primes p with P(p-1) 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 (list; graph; refs; listen; history; text; internal format)
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(n-1) for all n > 5.

The b-file 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(p-1) with p prime.

LINKS

Zhi-Wei 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(2-1) = 1 is not prime, but P(3-1) = 2 is prime.

a(2) = 5 since P(5-1) = 5 is prime.

a(3) = 7 since P(7-1) = 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

Zhi-Wei Sun, Dec 28 2013

STATUS

approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)