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

Author

Zhi-Wei Sun, Dec 29 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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}]

Formula

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