

A004090


Sum of digits of Fibonacci numbers.


24



0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 10, 17, 9, 8, 17, 7, 24, 22, 19, 14, 24, 20, 17, 28, 27, 19, 19, 29, 21, 23, 17, 31, 30, 34, 37, 35, 27, 35, 44, 43, 24, 31, 46, 41, 33, 29, 35, 37, 54, 55, 46, 29, 48, 41, 53, 58, 48, 52, 73, 44, 54, 53, 62, 61, 51, 67, 73, 59
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OFFSET

0,4


COMMENTS

a(n) and Fib(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fib(n) mod 9) A007887(n). Thus (a(n) mod 9) is periodic with the Pisano period A001175(9) = 24.  Hieronymus Fischer, Jun 25 2007
It appears that a(n)n stays negative for n > 5832, which explains why A020995 is finite.  T. D. Noe, Mar 19 2012


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000
T. D. Noe, Plot of a(n)n for n = 0..100000


FORMULA

a(n) = Fib(n)  9*sum{k>0, floor(Fib(n)/10^k)}.  Hieronymus Fischer, Jun 25 2007
a(n) = A007953(A000045(n)).  Reinhard Zumkeller, Nov 17 2014


MATHEMATICA

Table[Plus@@IntegerDigits@(Fibonacci[n]), {n, 0, 90}] (* Vincenzo Librandi, Jun 18 2015 *)


PROG

(PARI) a(n)=sumdigits(fibonacci(n)) \\ Charles R Greathouse IV, Feb 03 2014
(Haskell)
a004090 = a007953 . a000045  Reinhard Zumkeller, Nov 17 2014
(MAGMA) [&+Intseq(Fibonacci(n)): n in [0..80] ]; // Vincenzo Librandi, Jun 18 2015


CROSSREFS

Cf. A000045, A030132, A007953, A246558, A261587, A068500.
Sequence in context: A007887 A105472 A030132 * A104205 A267758 A333301
Adjacent sequences: A004087 A004088 A004089 * A004091 A004092 A004093


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



