A132636 a(n) = Fibonacci(n) mod n^3.

0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 1685, 7063, 4323, 4896, 12525, 15937, 19271, 10483, 2060, 22040, 5674, 15621, 2752, 3807, 9340, 432, 46989, 19305, 11932, 62155, 31899, 12088, 22273, 3677, 32420

Offset: 1

Author

Hieronymus Fischer, Aug 24 2007

Keywords

• nonn

Comments

a(1) = 0; for n=2 to 20, a(n) = A000045(n); otherwise for instance, see example. - Michel Marcus, Jul 15 2013

Examples

			a(21) = 1685, since Fibonacci(21) = 10946 == 1685 (mod 21^3).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A000578, A023173.

Programs

Mathematica

Table[Mod[Fibonacci[n],n^3],{n,45}] (* James C. McMahon, Mar 08 2025 *)

PARI

a(n) = fibonacci(n) % n^3 \\ Michel Marcus, Jul 15 2013

PARI

a(n)=lift((Mod([1,1;1,0],n^3))^n)[1,2] \\ Charles R Greathouse IV, Jul 18 2013

Formula

a(n) = A000045(n) mod A000578(n).