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 A234644 Primes p with q(p) - 1 also prime, where q(.) is the strict partition function (A000009). 9

%I

%S 5,11,13,17,19,23,41,43,53,59,79,103,151,191,269,277,283,373,419,521,

%T 571,577,607,829,859,1039,2503,2657,2819,3533,3671,4079,4153,4243,

%U 4517,4951,4987,5689,5737,5783,7723,8101,9137,9173,9241,9539,11467,12323,12697,15017,15277,15427,15803,16057,17959,18661

%N Primes p with q(p) - 1 also prime, where q(.) is the strict partition function (A000009).

%C By the conjecture in A234615, this sequence should have infinitely many terms.

%C See A234647 for primes of the form q(p) - 1 with p prime.

%C See also A234530 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A234644/b234644.txt">Table of n, a(n) for n = 1..140</a>

%H Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014

%e a(1) = 5 since neither q(2) - 1 = 0 nor q(3) - 1 = 1 is prime, but q(5) - 1 = 2 is prime.

%e a(2) = 11 since q(7) - 1 = 4 is composite, but q(11) - 1 = 11 is prime.

%t q[k_]:=q[k]=PrimeQ[PartitionsQ[Prime[k]]-1]

%t n=0;Do[If[q[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10^5}]

%Y Cf. A000009, A000040, A234470, A234475, A234514, A234530, A234567, A234569, A234572, A234615, A234647.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Dec 29 2013

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Last modified May 21 17:27 EDT 2019. Contains 323444 sequences. (Running on oeis4.)