cp's OEIS Frontend

A233393 Primes of the form 2^k - 1 + q(m) with k > 0 and m > 0, where q(.) is the strict partition function (A000009).

%I A233393 #15 Aug 05 2019 09:27:49
%S A233393 2,3,5,7,11,13,17,19,23,29,37,41,43,47,53,61,67,71,73,79,83,101,107,
%T A233393 109,127,131,137,139,149,157,167,173,181,191,193,199,223,229,257,263,
%U A233393 269,271,277,293,311,331,347,349,359,383,397,421,449,463,467,479,521,523,557,587
%N A233393 Primes of the form 2^k - 1 + q(m) with k > 0 and m > 0, where q(.) is the strict partition function (A000009).
%C A233393 Conjecture: The sequence has infinitely many terms.
%C A233393 This follows from the conjecture in A233390.
%H A233393 Zhi-Wei Sun, <a href="/A233393/b233393.txt">Table of n, a(n) for n = 1..542</a>
%H A233393 Z.-W. Sun, <a href="http://arxiv.org/abs/1312.1166">On a^n+ bn modulo m</a>, arXiv preprint arXiv:1312.1166 [math.NT], 2013-2014.
%e A233393 a(1) = 2 since 2^1 - 1 + q(1) = 1 + 1 = 2.
%e A233393 a(2) = 3 since 2^1 - 1 + q(3) = 1 + 2 = 3.
%e A233393 a(3) = 5 since 2^2 - 1 + q(3) = 3 + 2 = 5.
%t A233393 Pow[n_]:=Pow[n]=Mod[n,2]==0&&2^(IntegerExponent[n,2])==n
%t A233393 n=0
%t A233393 Do[Do[If[Pow[Prime[m]-PartitionsQ[k]+1],
%t A233393 n=n+1;Print[n," ",Prime[m]];Goto[aa]];If[PartitionsQ[k]>=Prime[m],Goto[aa]];Continue,{k,1,2*Prime[m]}];
%t A233393 Label[aa];Continue,{m,1,110}]
%Y A233393 Cf. A000040, A000225, A232504, A233307, A233346, A233359, A233360, A233390.
%K A233393 nonn
%O A233393 1,1
%A A233393 _Zhi-Wei Sun_, Dec 08 2013