A194363 Lucas entry points: smallest m >= 0 such that the n-th prime divides Lucas(m), or -1 if there is no such m.

0, 2, -1, 4, 5, -1, -1, 9, 12, 7, 15, -1, 10, 22, 8, -1, 29, -1, 34, 35, -1, 39, 42, -1, -1, 25, 52, 18, -1, -1, 64, 65, -1, 23, -1, 25, -1, 82, 84, -1, 89, 45, 95, -1, -1, 11, 21, 112, 114, 57, -1, 119, 60, 125, -1, 44, -1, 135, -1, 14, 142, -1, 22, 155, -1

Offset: 1

Author

T. D. Noe, Oct 09 2011

Keywords

• sign

Comments

The -1 terms are for the primes in A053028. Note that 2 divides the zeroth Lucas number. In the plots, the uppermost line consists of the odd primes in A000057. Note that when a(n) > 0, then a(n) = A001602(n)/2.

Links

• T. D. Noe, Table of n, a(n) for n = 1..2000
• T. D. Noe, Another plot of this sequence

Crossrefs

Cf. A000204 (Lucas numbers), A001602 (Fibonacci entry points), A223486 (Lucas entry points), A000040 (prime numbers).

Programs

Mathematica

lim = 100; luc = LucasL[Range[0, Prime[lim]]]; Table[s = Select[Range[p], Mod[luc[[#]], p] == 0 &, 1]; If[s == {}, -1, s[[1]] - 1], {p, Prime[Range[lim]]}]

Formula

a(n) = A223486(A000040(n)). - Jon Maiga, Jul 01 2021