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

7,3

Links

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

Formula

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

Example

a(9) = 34 mod 7 = 6.

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 *)

Crossrefs

Cf. A000045, A004090, A007953.

Sequence in context: A195713 A306712 A109063 * A193178 A084448 A256596

Adjacent sequences: A110387 A110388 A110389 * A110391 A110392 A110393

Keyword

base,easy,nonn

Author

Amarnath Murthy, Jul 27 2005

Extensions

More terms from Ryan Propper, Aug 14 2005

More terms from Harvey P. Dale, Dec 05 2015

Status

approved