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A234572 Primes of the form P(p-1), where p is a prime and P(.) is the partition function (A000041). 6
2, 5, 11, 17977, 790738119649411319, 2058791472042884901563, 27833079238879849385687, 8121368081058512888507057, 675004412390512738195023734124239, 1398703012615213588677365804960180341, 16193798232344933888778097136641377589301, 204931453786129197483756438132982529754356479553, 3019564607799532159016586951616642980389816614848623, 22757918197082858017617136646280039394687006502870793231847, 1078734573992480956821414895441907729656949308800686938161281 (list; graph; refs; listen; history; text; internal format)
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 * A109623 A317406 A286466

Adjacent sequences:  A234569 A234570 A234571 * A234573 A234574 A234575

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Dec 28 2013

STATUS

approved

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Last modified May 21 09:15 EDT 2019. Contains 323441 sequences. (Running on oeis4.)