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A004090
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Sum of digits of Fibonacci numbers.
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27
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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
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0,4
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = Fibonacci(n) - 9*Sum_{k>0} floor(Fibonacci(n)/10^k). - Hieronymus Fischer, Jun 25 2007
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MATHEMATICA
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Table[Plus@@IntegerDigits@(Fibonacci[n]), {n, 0, 90}] (* Vincenzo Librandi, Jun 18 2015 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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