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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 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

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