A235357 Primes of the form q(m) - 1 with m - 1 and m + 1 both prime, where q(.) is the strict partition function (A000009).

3, 4919887991, 28253252977151, 20964758762885249107967, 47573613463034233651199, 12796446358667905839216959, 10712934162879755412803989317623807, 33014011446550388413724585366558782455972162239

Offset: 1

Author

Zhi-Wei Sun, Jan 07 2014

Keywords

• nonn
• hard

Comments

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

See A235346 for a list of known numbers m with m - 1, m + 1 and q(m) - 1 all prime.

See also A235356 for a similar sequence.

Examples

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

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A000009, A000040, A014574, A235343, A235344, A235346, A235356.

Programs

Mathematica

g[n_]:=A235346(n)
Table[PartitionsQ[g[n]]-1,{n,1,10}]

Formula

a(n) = A000009(A235346(n)) - 1.