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

1,1

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.

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A227743 A335752 A343768 * A347593 A120426 A077201

Adjacent sequences: A235353 A235354 A235355 * A235357 A235358 A235359

Keyword

nonn

Author

Zhi-Wei Sun, Jan 07 2014

Status

approved