OFFSET
1,2
COMMENTS
Can the arithmetic mean of the tribonacci numbers (T(0)+...+T(k-1)) / k be an integer?
The arithmetic means are integers for the first 1, 2, 47, 53, 94, 103, 106, ... (A141579) tribonacci numbers. - R. J. Mathar, Aug 04 2008
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Numbers k such that (T(0)^2+ T(1)^2+ ... + T(k-1)^2) / k is an integer, where T(i) = i-th tribonacci number.
MATHEMATICA
With[{m = 1000}, Position[Accumulate[LinearRecurrence[{1, 1, 1}, {0, 0, 1}, m]^2] / Range[m], _?IntegerQ] // Flatten] (* Amiram Eldar, Jul 04 2025 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Jul 27 2008
EXTENSIONS
a(1)-a(2) inserted and a(32) onwards added by R. J. Mathar, Aug 04 2008
STATUS
approved