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A020995
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Numbers n such that sum of digits of Fibonacci(n) is n.
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0
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0, 1, 5, 10, 31, 35, 62, 72, 175, 180, 216, 251, 252, 360, 494, 504, 540, 946, 1188, 2222
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Since the number of digits in the n-th Fibonacci number ~ n*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*n (where n is the number of the digits). - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 12 2006
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REFERENCES
| David Terr, Fibonacci Quarterly, August 1996, page 349-355.
Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page 209.
L. Bankoff, A Fibonacci Curiosity, Fibonacci Quarterly 14 (1976), page 17. [From Ron Knott (enquiry(AT)ronknott.com), Oct 30 2010]
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EXAMPLE
| Fibonacci(10) = 55 and 5+5 = 10.
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MATHEMATICA
| Do[ If[ Apply[ Plus, IntegerDigits[ Fibonacci[n]]] == n, Print[n]], {n, 1, 10^5} ]
Do[ If[ Mod[ Fibonacci[n], 9] == Mod[n, 9], If[ Plus @@ IntegerDigits[ Fibonacci[n]] == n, Print[n]]], {n, 0, 10^6}] (from Robert G. Wilson v)
Do[ If[ Mod[ Fibonacci[n], 9] == Mod[n, 9], If[ Plus @@ IntegerDigits[ Fibonacci[n]] == n, Print[n]]], {n, 0, 10^6}] (from Robert G. Wilson v)
Select[Range[0, 10^5], Plus @@ IntegerDigits[Fibonacci[ # ]] == # &] [From Ron Knott (enquiry(AT)ronknott.com), Oct 30 2010]
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CROSSREFS
| Cf. A067515.
Sequence in context: A056422 A032296 A052648 * A174467 A005201 A094234
Adjacent sequences: A020992 A020993 A020994 * A020996 A020997 A020998
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KEYWORD
| nonn,base
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AUTHOR
| Sven-H.Simon(AT)t-online.de (Sven Simon)
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