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A233360 Primes of the form L(k) + q(m) with k > 0 and m > 0, where L(k) is the k-th Lucas number (A000204), and q(.) is the strict partition function (A000009).

%I A233360 #7 Dec 08 2013 09:31:59
%S A233360 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,79,83,101,
%T A233360 103,107,127,131,149,151,193,199,211,223,227,229,233,239,241,251,257,
%U A233360 263,269,307,337,347,349,379,397,401,419,421,449,463,487,523,541,571,643,647,661
%N A233360 Primes of the form L(k) + q(m) with k > 0 and m > 0, where L(k) is the k-th Lucas number (A000204), and q(.) is the strict partition function (A000009).
%C A233360 Conjecture: The sequence has infinitely many terms.
%C A233360 This follows from the conjecture in A233359.
%H A233360 Zhi-Wei Sun, <a href="/A233360/b233360.txt">Table of n, a(n) for n = 1..270</a>
%e A233360 a(1) = 2 since L(1) + q(1) = 1 + 1 = 2.
%e A233360 a(2) = 3 since L(1) + q(3) = 1 + 2 = 3.
%e A233360 a(3) = 5 since L(2) + q(3) = 3 + 2 = 5.
%t A233360 n=0
%t A233360 Do[Do[If[LucasL[j]>=Prime[m],Goto[aa],
%t A233360 Do[If[PartitionsQ[k]==Prime[m]-LucasL[j],
%t A233360 n=n+1;Print[n," ",Prime[m]];Goto[aa]];If[PartitionsQ[k]>Prime[m]-LucasL[j],Goto[bb]];Continue,{k,1,2*(Prime[m]-LucasL[j])}]];
%t A233360 Label[bb];Continue,{j,1,2*Log[2,Prime[m]]}];
%t A233360 Label[aa];Continue,{m,1,125}]
%Y A233360 Cf. A000009, A000040, A000032, A000204, A232504, A233307, A233346, A233359.
%K A233360 nonn
%O A233360 1,1
%A A233360 _Zhi-Wei Sun_, Dec 08 2013