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A235344 Numbers m with m - 1, m + 1 and q(m) + 1 all prime, where q(.) is the strict partition function (A000009).

%I A235344 #88 Oct 19 2014 16:00:38
%S A235344 4,6,18,42,72,102,270,282,312,618,1032,1062,1320,1950,2082,3528,7350,
%T A235344 7488,10332,15138,17388,21600,40038,44700,134922,156258,187908,243708,
%U A235344 339138,389568,495360,610920,761712,911292,916218,943800,1013532,1217472,1312602
%N A235344 Numbers m with m - 1, m + 1 and q(m) + 1 all prime, where q(.) is the strict partition function (A000009).
%C A235344 Clearly, any term after the first term 4 is a multiple of 6. By part (i) of the conjecture in A235343, this sequence should have infinitely many terms. The prime q(a(51)) + 1 = q(3235368) + 1 has 1412 decimal digits.
%C A235344 See A235356 for primes of the form q(m) + 1 with m - 1 and m + 1 both prime.
%C A235344 See also A235346 for a similar sequence.
%H A235344 Zhi-Wei Sun, <a href="/A235344/b235344.txt">Table of n, a(n) for n = 1..51</a>
%H A235344 Zhi-Wei Sun, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;2a0328e6.1401">Twin primes and the strict partition function</a>, a message to Number Theory List, Jan. 15, 2014.
%H A235344 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A235344 a(1) = 4 since 4 - 1, 4 + 1 and q(4) + 1 = 3 are all prime.
%e A235344 a(2) = 6 since 6 - 1, 6 + 1 and q(6) + 1 = 5 are all prime.
%t A235344 f[k_]:=PartitionsQ[Prime[k]+1]+1
%t A235344 n=0;Do[If[PrimeQ[Prime[k]+2]&&PrimeQ[f[k]],n=n+1;Print[n," ",Prime[k]+1]],{k,1,10000}]
%Y A235344 Cf. A000009, A000040, A014574, A234530, A234569, A234644, A235343, A235346, A235356, A235357, A235358.
%K A235344 nonn,hard
%O A235344 1,1
%A A235344 _Zhi-Wei Sun_, Jan 06 2014