A110390 a(n) = F(n) mod s(n) where s(n) is the sum of the digits of the n-th Fibonacci number F(n).

1, 0, 6, 5, 4, 0, 1, 3, 1, 3, 13, 0, 9, 21, 6, 14, 13, 9, 13, 2, 1, 18, 18, 9, 1, 9, 2, 3, 30, 0, 12, 21, 38, 3, 27, 38, 2, 3, 2, 13, 3, 18, 34, 1, 5, 3, 28, 0, 1, 21, 14, 38, 1, 18, 40, 1, 2, 30, 65, 21, 34, 48, 64, 55, 45, 0, 49, 33, 60, 63, 3, 24, 5, 21, 2

Offset: 7

Author

Amarnath Murthy, Jul 27 2005

Keywords

• base
• easy
• nonn

Examples

			a(9) = 34 mod 7 = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..10000

Crossrefs

Cf. A000045, A004090, A007953.

Programs

Maple

a:= n-> (f-> irem(f, add(i, i=convert(f, base, 10))))(combinat[fibonacci](n)):
seq(a(n), n=7..100);  # Alois P. Heinz, Jan 05 2022

Mathematica

Do[k = Fibonacci[n]; Print[Mod[k, Plus @@ IntegerDigits[k]]], {n, 7, 56}] (* Ryan Propper, Aug 14 2005 *)
Mod[#,Total[IntegerDigits[#]]]&/@Fibonacci[Range[7,70]] (* Harvey P. Dale, Dec 05 2015 *)

Formula

a(n) = A000045(n) mod A007953(A000045(n)) = A000045(n) mod A004090(n).

Extensions

More terms from Ryan Propper, Aug 14 2005

More terms from Harvey P. Dale, Dec 05 2015