A278834 Record values of A004090(n) - n, where A004090 is the sum of digits of the Fibonacci numbers A000045.

0, 2, 6, 8, 15, 30, 32, 40, 44, 46, 51, 57, 92

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.

Links

Table of n, a(n) for n=1..13.

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

Cf. A000045 (Fibonacci numbers), A004090 (their digital sums), A278833 (the indices corresponding to the record values listed here), A264935.

Sequence in context: A093005 A049818 A066189 * A336896 A306906 A174658

Adjacent sequences: A278831 A278832 A278833 * A278835 A278836 A278837

Keyword

nonn,base,fini,full

Author

M. F. Hasler, Dec 28 2016

Status

approved