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

1,1

Comments

Conjecture: The sequence has infinitely many terms.

This follows from the conjecture in A233359.

Links

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A228296 A176165 A196230 * A234960 A118850 A322443

Adjacent sequences: A233357 A233358 A233359 * A233361 A233362 A233363

Keyword

nonn

Author

Zhi-Wei Sun, Dec 08 2013

Status

approved