A234572 Primes of the form P(p-1), where p is a prime and P(.) is the partition function (A000041).

2, 5, 11, 17977, 790738119649411319, 2058791472042884901563, 27833079238879849385687, 8121368081058512888507057, 675004412390512738195023734124239, 1398703012615213588677365804960180341, 16193798232344933888778097136641377589301, 204931453786129197483756438132982529754356479553, 3019564607799532159016586951616642980389816614848623, 22757918197082858017617136646280039394687006502870793231847, 1078734573992480956821414895441907729656949308800686938161281

Offset

1,1

Comments

Though the primes in this sequence are very rare, by the conjecture in A234567 there should be infinitely many such primes.

See A234569 for a list of known primes p with P(p-1) also prime.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..50

Formula

a(n) = A000041(A234569(n)-1).

Example

a(1) = 2 since 2 = P(3-1) with 2 and 3 both prime.
a(2) = 5 since 5 = P(5-1) with 5 prime.
a(3) = 11 since 11 = P(7-1) with 7 and 11 both prime.

Mathematica

p[n_]:= A234569(n)
Table[PartitionsP[p[n]-1], {n, 1, 15}]

Crossrefs

Cf. A000040, A000041, A049575, A233346, A234470, A234475, A234514, A234530, A234567, A234569

Sequence in context: A158997 A101828 A071293 * A341804 A109623 A317406

Adjacent sequences: A234569 A234570 A234571 * A234573 A234574 A234575

Keyword

nonn

Author

Zhi-Wei Sun, Dec 28 2013

Status

approved