A004090 - OEIS

A004090

Sum of digits of Fibonacci numbers.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

a(n) and Fibonacci(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fibonacci(n) mod 9) A007887(n). Thus (a(n) mod 9) is periodic with 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) = Fibonacci(n) - 9*Sum_{k>0} floor(Fibonacci(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