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A278834 Record values of A004090(n) - n, where A004090 is the sum of digits of the Fibonacci numbers A000045. 2
0, 2, 6, 8, 15, 30, 32, 40, 44, 46, 51, 57, 92 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base,fini,full
AUTHOR
M. F. Hasler, Dec 28 2016
STATUS
approved

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Last modified June 20 18:51 EDT 2024. Contains 373532 sequences. (Running on oeis4.)