A234366 -id:A234366 - cp's OEIS frontend

A234530 Primes p with q(p) + 1 also prime, where q(.) is the strict partition function (A000009).

2, 3, 11, 13, 29, 37, 47, 71, 79, 89, 103, 127, 131, 179, 181, 197, 233, 271, 331, 379, 499, 677, 691, 757, 887, 911, 1019, 1063, 1123, 1279, 1429, 1531, 1559, 1637, 2251, 2719, 3571, 4007, 4201, 4211, 4297, 4447, 4651, 4967, 5953, 6131, 7937, 8233, 8599, 8819, 9013, 11003, 11093, 11813, 12251, 12889, 12953, 13487, 13687, 15259

Offset: 1

Zhi-Wei Sun, Dec 27 2013

nonn

By the conjecture in A234514, this sequence should have infinitely many terms.
It seems that a(n+1) < a(n) + a(n-1) for all n > 4.
See A234366 for primes of the form q(p) + 1 with p prime.
See also A234644 for a similar sequence.

			a(1) = 2 since 2 and q(2) + 1 = 2 are both prime.
a(2) = 3 since 3 and q(3) + 1 = 3 are both prime.
a(3) = 11 since 11 and q(11) + 1 = 13 are both prime.

Zhi-Wei Sun, Table of n, a(n) for n = 1..150

Cf. A000009, A000040, A233346, A233393, A234366, A234470, A234475, A234514, A234567, A234569, A234572, A234615, A234644, A234647

n=0;Do[If[PrimeQ[PartitionsQ[Prime[k]]+1],n=n+1;Print[n," ",Prime[k]]],{k,1,10^5}]
Select[Prime[Range[2000]],PrimeQ[PartitionsQ[#]+1]&] (* Harvey P. Dale, Apr 23 2017 *)

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

Original entry on oeis.org

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

Zhi-Wei Sun, Dec 29 2013

nonn

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.

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

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

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

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

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

cp's OEIS Frontend

A234530 Primes p with q(p) + 1 also prime, where q(.) is the strict partition function (A000009).

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