

A111058


Numbers k such that the average of the first k Lucas numbers is an integer.


1



1, 2, 8, 12, 20, 24, 48, 60, 68, 72, 92, 96, 120, 140, 144, 188, 192, 200, 212, 216, 240, 288, 300, 332, 336, 360, 384, 428, 432, 440, 452, 480, 500, 548, 576, 600, 648, 660, 668, 672, 680, 692, 696, 720, 768, 780, 788, 812, 864, 908, 932, 960
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OFFSET

1,2


COMMENTS

A111035 is the equivalent for Fibonacci numbers and has many elements in common with this sequence. T. D. Noe, who extended this sequence, noticed that, for some reason, 24 divides many of those k.


LINKS

Table of n, a(n) for n=1..52.


FORMULA

k such that (Sum_{i=0..k} A000032(i))/k is an integer.


EXAMPLE

a(1) = 1 because the first Lucas number is 2 and 2/1 = 2, an integer.
a(2) = 3 because the sum of the first three Lucas numbers is 2 + 1 + 3 = 6 and hence the average is 6/3 = 2, an integer.
a(6) = 24 because the average of the first 24 Lucas numbers is 2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47 + 76 + 123 + 199 + 322 + 521 + 843 + 1364 + 2207 + 3571 + 5778 + 9349 + 15127 + 24476 + 39603 + 64079) / 24 = 6990, an integer.


MATHEMATICA

Lucas[n_] := Fibonacci[n+1]+Fibonacci[n1]; lst={}; s=0; Do[s=s+Lucas[n]; If[Mod[s, n]==0, AppendTo[lst, n]], {n, 1000}]; lst (* T. D. Noe *)


CROSSREFS

Cf. A000032, A111035.
Sequence in context: A108987 A035405 A280867 * A063622 A162152 A280252
Adjacent sequences: A111055 A111056 A111057 * A111059 A111060 A111061


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Oct 07 2005


STATUS

approved



