A140972 Numbers n such that arithmetic mean of squares of first n Lucas numbers is an integer.

1, 10, 12, 24, 36, 48, 60, 72, 96, 108, 120, 144, 168, 180, 192, 216, 240, 250, 288, 300, 324, 336, 360, 384, 432, 442, 480, 504, 540, 550, 552, 576, 600, 612, 624, 648, 660, 672, 684, 720, 768, 840, 864, 900, 960, 972, 1008, 1068, 1080, 1104, 1152, 1176, 1200

Offset

1,2

Comments

The root mean square RMS(L(0),...,L(n-1)) is firstly an integer for n = 36.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

n such that (L(0)^2+ L(1)^2+ ... + L(n-1)^2) / n is an integer. L(i) i-th Lucas number.

Example

n=10 : (L(0)^2+...+L(9)^2)/10 = 935

Mathematica

With[{nn=1200}, Transpose[Select[Thread[{Range[nn], Accumulate[ LucasL[ Range[0, nn-1]]^2]}], IntegerQ[Last[#]/First[#]]&]][[1]]] (* Harvey P. Dale, Jul 15 2012 *)

Crossrefs

Cf. A000032, A140480.

Sequence in context: A235686 A087697 A241177 * A108901 A372488 A073083

Adjacent sequences: A140969 A140970 A140971 * A140973 A140974 A140975

Keyword

easy,nonn

Author

Ctibor O. Zizka, Jul 27 2008

Extensions

Inserted 1 and extended from 48 on, R. J. Mathar, Aug 04 2008

Status

approved