A278833 Indices of records of A004090(n) - n, where A004090 is the sum of digits of the Fibonacci numbers A000045.

0, 6, 11, 16, 58, 178, 195, 273, 695, 862, 989, 2477, 2619

Offset: 1

Author

M. F. Hasler, Dec 28 2016

Keywords

• nonn
• base
• fini
• full

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 (see A278834). So the sequence of indices of records in the weak sense of >= would be (0, 1, 5, 6, 11, 16, 58, 83, 156, 178, 195, 273, 512, 695, 862, 989, 2477, 2619).

Conjectured to be finite and complete. Indeed it appears that 0.9*n < A004090(n) < n for all sufficiently large n.

Crossrefs

Cf. A000045 (Fibonacci numbers), A004090 (their digital sums), A278834 (the record values corresponding to the indices listed here).

Except for the initial 0, this appears to be a subsequence of A264935.

Programs

Mathematica

Function[t, Flatten@ Map[First@ Position[t, #] - 1 &, Union@ Rest@ FoldList[Max, 0, t]]]@ Table[Plus @@ IntegerDigits@ Fibonacci@n - n, {n, 0, 10^4}] (* Michael De Vlieger, Dec 28 2016 *)

PARI

m=-1; for(k=0, 1e4, sumdigits(fibonacci(k))-k>m&&print1(k", ")+m=sumdigits(fibonacci(k))-k)