

A140972


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


2



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
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OFFSET

1,2


COMMENTS

The root mean square RMS(L(0),...,L(n1)) 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(n1)^2) / n is an integer. L(i) ith 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, nn1]]^2]}], IntegerQ[Last[#]/First[#]]&]][[1]]] (* Harvey P. Dale, Jul 15 2012 *)


CROSSREFS

Cf. A000032, A140480.
Sequence in context: A235686 A087697 A241177 * A108901 A073083 A129508
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



