OFFSET
1,3
COMMENTS
Since the number of digits in the k-th Fibonacci number ~ k*log_10(Golden Ratio), theoretically this sequence is infinite, but then the average density of those digits = ~ 0.208987. - Robert G. Wilson v
Robert Dawson of Saint Mary's University says it is likely that 2222 is the last term, as (assuming that the digits are equally distributed) the expected digit sum is ~ 0.9*k. - Stefan Steinerberger, Mar 12 2006 [Assuming that the average digit is (0+1+2+...+9)/10 = 9/2, the expected digit sum is ~ (9/2)*log_10((1+sqrt(5))/2)*k = 0.94044438...*k. - Jon E. Schoenfield, Aug 28 2022]
Bankoff's short paper lists the first seven terms. - T. D. Noe, Mar 19 2012
No more terms < 150000. - Manfred Scheucher, Aug 03 2015
If it exists, a(21) > 10^6. - Robert Price, May 26 2019
REFERENCES
Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page 209.
LINKS
Leon Bankoff, A Fibonacci Curiosity, Fibonacci Quarterly 14, Feb. 1976, p. 17.
Pat Ballew, Fibonacci Digit Sums, Pat's Blog, Sunday, 5 August 2012.
Manfred Scheucher, Sage Script
David Terr, On the Sums of Digits of Fibonacci Numbers, Fibonacci Quarterly 34, Aug. 1996, pp. 349-355.
EXAMPLE
Fibonacci(10) = 55 and 5+5 = 10.
MATHEMATICA
Do[ If[ Apply[ Plus, IntegerDigits[ Fibonacci[n]]] == n, Print[n]], {n, 1, 10^5} ] (* Sven Simon *)
Do[ If[ Mod[ Fibonacci[n], 9] == Mod[n, 9], If[ Plus @@ IntegerDigits[ Fibonacci[n]] == n, Print[n]]], {n, 0, 10^6}] (* Robert G. Wilson v *)
Select[Range[0, 10^5], Plus @@ IntegerDigits[Fibonacci[ # ]] == # &] (* Ron Knott, Oct 30 2010 *)
PROG
(PARI) isok(n) = sumdigits(fibonacci(n)) == n; \\ Michel Marcus, Feb 18 2015
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
STATUS
approved