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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
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
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
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