A160665 Numbers k such that the arithmetic mean of the first k Lucas numbers A000032 is an integer.

1, 3, 24, 48, 72, 96, 120, 144, 192, 216, 240, 288, 336, 360, 384, 406, 432, 480, 576, 600, 648, 672, 720, 768, 864, 936, 960, 1008, 1080, 1104, 1152, 1200, 1224, 1296, 1320, 1344, 1368, 1440, 1536, 1680, 1728, 1800, 1920, 1944, 2016, 2160, 2208, 2304

Offset

1,2

Comments

Numbers n such that sum(i=0..n, A000032(i))/(n+1) is an integer. - Robert G. Wilson v, May 25 2009

Why do the terms in A141767 so closely correspond to A160665? Except for n = 1, 3, 406, 44758, 341446, 1413286, 3170242, 4861698, 7912534, ..., n == 0 (mod 24). - Robert G. Wilson v, May 25 2009

Links

Table of n, a(n) for n=1..48.

Formula

{n: n | A001610(n)}. - R. J. Mathar, May 25 2009

Maple

A000032 := proc(n) option remember ; if n <= 1 then 2-n; else procname(n-1)+procname(n-2) ; fi; end: A001610 := proc(n) add(A000032(i), i=0..n-1) ; end: for n from 1 to 3000 do if A001610(n) mod n = 0 then printf("%d, ", n) ; fi; od: # R. J. Mathar, May 25 2009

Mathematica

lst = {}; a = 2; b = 1; s = 3; n = 3; While[n < 2447, c = a + b; s = s + c; If[Mod[c, n] == 0, AppendTo[lst, n]]; a = b; b = c; n++ ]; lst (* Robert G. Wilson v, May 25 2009 *)

Crossrefs

Cf. A000032, A111058, A140826, A140971, A140972.

Sequence in context: A278491 A363536 A293594 * A211034 A220868 A296273

Adjacent sequences: A160662 A160663 A160664 * A160666 A160667 A160668

Keyword

nonn

Author

Ctibor O. Zizka, May 22 2009

Extensions

More terms from R. J. Mathar and Robert G. Wilson v, May 25 2009

Status

approved