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Lucas entry points: smallest m >= 0 such that the n-th prime divides Lucas(m), or -1 if there is no such m.
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%I #21 Jul 02 2021 16:39:44

%S 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,

%T 25,52,18,-1,-1,64,65,-1,23,-1,25,-1,82,84,-1,89,45,95,-1,-1,11,21,

%U 112,114,57,-1,119,60,125,-1,44,-1,135,-1,14,142,-1,22,155,-1

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

%C 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.

%H T. D. Noe, <a href="/A194363/b194363.txt">Table of n, a(n) for n = 1..2000</a>

%H T. D. Noe, <a href="/A194363/a194363.png">Another plot of this sequence</a>

%F a(n) = A223486(A000040(n)). - _Jon Maiga_, Jul 01 2021

%t 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]]}]

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

%K sign

%O 1,2

%A _T. D. Noe_, Oct 09 2011