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a(n) = n - A004090(n), where A004090 is the sum of digits of the Fibonacci numbers A000045.
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%I #25 Apr 28 2018 03:14:22

%S 0,0,1,1,1,0,-2,3,5,2,0,-6,3,5,-3,8,-8,-5,-1,5,-4,1,5,-5,-3,6,7,-2,7,

%T 6,13,0,2,-1,-3,0,9,2,-6,-4,16,10,-4,2,11,16,11,10,-6,-6,4,22,4,12,1,

%U -3,8,5,-15,15,6,8,0,2,13,-2,-7,8,17,4,8,25,0,9,-8,10,10,-9,-2,21,-4,2,18,-15,12,-4,6,-10,19,-5,17,23,14,28,5,4,6,-3,16,-2

%N a(n) = n - A004090(n), where A004090 is the sum of digits of the Fibonacci numbers A000045.

%C Conjectured to increase to infinity. It appears that the slope of A004090(n) is roughly 0.93, at least in the range 0..10^5.

%C I conjecture that this sequence takes its minimum at a(2619) = -92. - _M. F. Hasler_, Dec 30 2016

%H M. F. Hasler, <a href="/A280185/b280185.txt">Table of n, a(n) for n = 0..100000</a>

%F a(n) = n - A004090(n) = n - A007953(A000045(n)).

%e a(2) = a(3) = 1 because A000045(2) = 1 = A004090(2), its digital sum, A000045(3) = 2 = A004090(3), and 2 - 1 = 3 - 2 = 1.

%t Table[n - Total@ IntegerDigits@ Fibonacci@ n, {n, 0, 99}] (* _Michael De Vlieger_, Dec 28 2016 *)

%o (PARI) A280185(n)=n-sumdigits(fibonacci(n))

%o /* To produce the b-file; can be used for searches or similar purpose, this is faster than to compute fib(n) anew for each term. */

%o b=-a=1;for(n=0,1e5,write("/tmp/A280185.txt",n" ",n-sumdigits(a=b+b=a)))

%Y Cf. A000045 (Fibonacci numbers), A004090 (their digital sums), A278834 & A278833 (record values of this sequence and corresponding indices), A264935.

%K sign,base

%O 0,7

%A _M. F. Hasler_, Dec 28 2016