|
Search: id:A020995
|
|
|
| A020995 |
|
Numbers n such that sum of digits of Fibonacci(n) is n. |
|
+0
1
|
|
| 0, 1, 5, 10, 31, 35, 62, 72, 175, 180, 216, 251, 252, 360, 494, 504, 540, 946, 1188, 2222
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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
|
|
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.
|
|
EXAMPLE
|
Fibonacci(10) = 55 and 5+5 = 10.
|
|
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)
|
|
CROSSREFS
|
Cf. A067515.
Sequence in context: A056422 A032296 A052648 this_sequence A005201 A094234 A052538
Adjacent sequences: A020992 A020993 A020994 this_sequence A020996 A020997 A020998
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
Sven-H.Simon(AT)t-online.de (Sven Simon)
|
|
|
Search completed in 0.002 seconds
|
