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).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 127, 131, 149, 151, 193, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 307, 337, 347, 349, 379, 397, 401, 419, 421, 449, 463, 487, 523, 541, 571, 643, 647, 661

Offset: 1

Author

Zhi-Wei Sun, Dec 08 2013

Keywords

• nonn

Comments

Conjecture: The sequence has infinitely many terms.

This follows from the conjecture in A233359.

Examples

			a(1) = 2 since L(1) + q(1) = 1 + 1 = 2.
a(2) = 3 since L(1) + q(3) = 1 + 2 = 3.
a(3) = 5 since L(2) + q(3) = 3 + 2 = 5.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..270

Crossrefs

Cf. A000009, A000040, A000032, A000204, A232504, A233307, A233346, A233359.

Programs

Mathematica

n=0
Do[Do[If[LucasL[j]>=Prime[m],Goto[aa],
Do[If[PartitionsQ[k]==Prime[m]-LucasL[j],
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])}]];
Label[bb];Continue,{j,1,2*Log[2,Prime[m]]}];
Label[aa];Continue,{m,1,125}]