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

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, 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.

Crossrefs

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

Programs

Mathematica

Union@ Rest@ FoldList[Max, 0, #] &@ 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(m=sumdigits(fibonacci(k))-k,","))