A235356 Primes of the form q(m) + 1 with m - 1 and m + 1 both prime, where q(.) is the strict partition function (A000009).

3, 5, 47, 1427, 36353, 525017, 24782061071, 46193897033, 207839472391, 58195383726460417, 20964758762885249107969, 47573613463034233651201, 35940172290335689735986241, 39297101749677990678763409480449, 538442167350331131544523981355841

Offset: 1

Author

Zhi-Wei Sun, Jan 07 2014

Keywords

• nonn

Comments

Though the primes in this sequence are very rare, by part (i) of the conjecture in A235343 there should be infinitely many such primes.

See A235344 for a list of known numbers m with m - 1, m + 1 and q(m) + 1 all prime.

See also A235357 for a similar sequence.

Examples

			a(1) = 3 since 3 = q(4) + 1 with 4 - 1 and 4 + 1 both prime.
a(2) = 5 since 5 = q(6) + 1 with 6 - 1 and 6 + 1 both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..30

Crossrefs

Cf. A000009, A000040, A014574, A235343, A235344, A235346, A235357.

Programs

Mathematica

f[n_]:=A235344(n)
Table[PartitionsQ[f[n]]+1,{n,1,15}]

Formula

a(n) = A000009(A235344(n)) + 1.