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A030132
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Digital root of Fibonacci(n).
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12
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0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Every other (a(0),a(1)) pair of nonzero digits enters a cycle of length 24, except for (3,3) which enters a cycle of length 8 and (9,9) which is periodic of length 1. - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 29 2005
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REFERENCES
| S. Marivani and others, Problem 10974, Amer. Math. Monthly, 111 (No. 7, 2004), 628.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Colm Mulcahy, Gibonacci Bracelets.
Marc Renault, The Fibonacci sequence modulo m
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FORMULA
| a(n+1) = sum of digits of (a(n) + a(n-1)).
Periodic with period 24 given by {1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9}
a(n+1) = sum of digits of (a(n) + a(n-1)). a(n+1) = A007953(a(n) + a(n-1)). - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 29 2005
a(n) + a(n+1) = A010077(n+4); a(A017641(n)) = 9. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 04 2007
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MATHEMATICA
| digitalRoot[n_Integer?Positive] := FixedPoint[Plus@@IntegerDigits[#]&, n]; Table[If[n==0, 0, digitalRoot[Fibonacci[n]]], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, May 02 2011 *)
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PROG
| (Haskell)
a030132 n = a030132_list !! n
a030132_list =
0 : 1 : map a007953 (zipWith (+) a030132_list (tail a030132_list))
-- Reinhard Zumkeller, Aug 20 2011
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CROSSREFS
| Cf. A000045 (Fibonacci numbers), A010888 (digital roots), A004090, A007953, A030133.
Sequence in context: A098906 A007887 A105472 * A004090 A104205 A166015
Adjacent sequences: A030129 A030130 A030131 * A030133 A030134 A030135
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KEYWORD
| nonn,base,easy,nice
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AUTHOR
| youngelder(AT)webtv.net (Ana)
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2004
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