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

Author

Ctibor O. Zizka, May 22 2009

Keywords

• nonn

Comments

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

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000032, A001610, A111058, A140826, A140971, A140972.

Programs

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 *)

Formula

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

Extensions

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