

A233360


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


4



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
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OFFSET

1,1


COMMENTS

Conjecture: The sequence has infinitely many terms.
This follows from the conjecture in A233359.


LINKS

ZhiWei 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

ZhiWei Sun, Dec 08 2013


STATUS

approved



