OFFSET
1,2
COMMENTS
For indices n = 1, 5, 83, 156 and 512, the value of the difference A004090(n) - n is the same as for the preceding record, namely (0, 0, 15, 15, 40), respectively. So the sequence of records in the weak sense of >= would be (0, 0, 0, 2, 6, 8, 15, 15, 15, 30, 32, 40, 40, 44, 46, 51, 57, 92).
Conjectured to be finite and complete. Indeed it appears that 0.9*n < A004090(n) < n for all sufficiently large n.
MATHEMATICA
Union@ Rest@ FoldList[Max, 0, #] &@ Table[Plus @@ IntegerDigits@ Fibonacci@ n - n, {n, 0, 10^4}] (* Michael De Vlieger, Dec 28 2016 *)
PROG
(PARI) m=-1; for(k=0, 1e4, sumdigits(fibonacci(k))-k>m && print1(m=sumdigits(fibonacci(k))-k, ", "))
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
M. F. Hasler, Dec 28 2016
STATUS
approved