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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
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
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}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 28 2013
STATUS
approved