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%I #40 Oct 24 2023 19:43:06
%S 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,
%T 29,21,23,17,31,30,34,37,35,27,35,44,43,24,31,46,41,33,29,35,37,54,55,
%U 46,29,48,41,53,58,48,52,73,44,54,53,62,61,51,67,73,59
%N Sum of digits of Fibonacci numbers.
%C 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
%C It appears that a(n) - n stays negative for n > 5832, which explains why A020995 is finite. - _T. D. Noe_, Mar 19 2012
%H T. D. Noe, <a href="/A004090/b004090.txt">Table of n, a(n) for n = 0..10000</a>
%H T. D. Noe, <a href="/A004090/a004090_1.gif">Plot of a(n)-n for n = 0..100000</a>
%F a(n) = Fibonacci(n) - 9*Sum_{k>0} floor(Fibonacci(n)/10^k). - _Hieronymus Fischer_, Jun 25 2007
%F a(n) = A007953(A000045(n)). - _Reinhard Zumkeller_, Nov 17 2014
%t Table[Plus@@IntegerDigits@(Fibonacci[n]), {n, 0, 90}] (* _Vincenzo Librandi_, Jun 18 2015 *)
%o (PARI) a(n)=sumdigits(fibonacci(n)) \\ _Charles R Greathouse IV_, Feb 03 2014
%o (Haskell)
%o a004090 = a007953 . a000045 -- _Reinhard Zumkeller_, Nov 17 2014
%o (Magma) [&+Intseq(Fibonacci(n)): n in [0..80] ]; // _Vincenzo Librandi_, Jun 18 2015
%Y Cf. A000045, A030132, A007953, A246558, A261587, A068500.
%K nonn,base,easy
%O 0,4
%A _N. J. A. Sloane_
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