A235357 - OEIS

%I #17 Oct 19 2014 06:26:25

%S 3,4919887991,28253252977151,20964758762885249107967,

%T 47573613463034233651199,12796446358667905839216959,

%U 10712934162879755412803989317623807,33014011446550388413724585366558782455972162239

%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 (ii) of the conjecture in A235343, there should be infinitely many such primes.

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

%C See also A235356 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A235357/b235357.txt">Table of n, a(n) for n = 1..25</a>

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

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

%t g[n_]:=A235346(n)

%t Table[PartitionsQ[g[n]]-1,{n,1,10}]

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

%K nonn,hard

%O 1,1

%A _Zhi-Wei Sun_, Jan 07 2014