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A132634
a(n) = Fibonacci(n) mod n^2.
5
0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 0, 64, 181, 160, 219, 152, 316, 210, 365, 362, 287, 91, 288, 25, 389, 317, 291, 378, 440, 869, 261, 574, 339, 765, 432, 443, 533, 1285, 1355, 1641, 1504, 85, 1741, 20, 551, 1832, 576, 1457, 1525, 389, 803, 2066, 332, 1820, 245
OFFSET
1,3
COMMENTS
a(n)=0 for n=1 and n=12 only (conjecture).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Hieronymus Fischer)
EXAMPLE
a(13) = 64, since Fibonacci(13) = 233 == 64 (mod 13^2).
MAPLE
p:= (M, n, k)-> map(x-> x mod k, `if`(n=0, <<1|0>, <0|1>>,
`if`(n::even, p(M, n/2, k)^2, p(M, n-1, k).M))):
a:= n-> p(<<0|1>, <1|1>>, n, n^2)[1, 2]:
seq(a(n), n=1..80);
MATHEMATICA
Table[Mod[Fibonacci[n], n^2], {n, 200}] (* Vladimir Joseph Stephan Orlovsky, Nov 28 2010 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Aug 24 2007
STATUS
approved