A234647 Primes of the form q(p) - 1, where p is a prime and q(.) is the strict partition function (A000009).

2, 11, 17, 37, 53, 103, 1259, 1609, 5119, 9791, 70487, 570077, 20792119, 281138047, 23515017983, 35692320959, 48626519093, 3626048321047, 27077619952639, 1651411233432319, 10743948315198451, 13378670620050079, 39413984631175423, 58553713102334907283, 145464242180631569963, 25408177717067357968543, 1374387931601409538722802926765483199, 20557774525717988142856527912112710143, 326033386646595458662191828888146112979, 27403889354101748193301659902924397784656229

Offset

1,1

Comments

Though the primes in this sequence are very rare, by the conjecture in A234615 there should be infinitely many such primes.

See A234644 for a list of known primes p with q(p) - 1 prime.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Formula

a(n) = A000009(A234615(n)) - 1.

Maple

a(1) = 2 since 2 = q(5) - 1 with 2 and 5 both prime.

Mathematica

p[n_]:=A234615(n)
Table[PartitionsQ[p[n]]-1, {n, 1, 30}]

Crossrefs

Cf. A000009, A000040, A234366, A234470, A234475, A234514, A234530, A234567, A234569, A234572, A234615, A234644

Sequence in context: A091735 A252657 A296053 * A106949 A236687 A187762

Adjacent sequences: A234644 A234645 A234646 * A234648 A234649 A234650

Keyword

nonn

Author

Zhi-Wei Sun, Dec 29 2013

Status

approved