A132634 a(n) = Fibonacci(n) mod n^2.

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

Author

Hieronymus Fischer, Aug 24 2007

Keywords

• nonn

Comments

a(n)=0 for n=1 and n=12 only (conjecture).

Examples

			a(13) = 64, since Fibonacci(13) = 233 == 64 (mod 13^2).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Hieronymus Fischer)

Crossrefs

Cf. A000045, A023173, A236395.

Programs

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 *)