A235356 - OEIS

%I #22 Oct 19 2014 15:10:26

%S 3,5,47,1427,36353,525017,24782061071,46193897033,207839472391,

%T 58195383726460417,20964758762885249107969,47573613463034233651201,

%U 35940172290335689735986241,39297101749677990678763409480449,538442167350331131544523981355841

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

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

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

%C See also A235357 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A235356/b235356.txt">Table of n, a(n) for n = 1..30</a>

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

%e a(1) = 3 since 3 = q(4) + 1 with 4 - 1 and 4 + 1 both prime.

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

%t f[n_]:=A235344(n)

%t Table[PartitionsQ[f[n]]+1,{n,1,15}]

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 07 2014