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Search: id:A079344
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| A079344 |
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F(n) mod 8, where F(n)=A000045(n) is the n-th Fibonacci number. |
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+0
9
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| 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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P. Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Q. 43 (No. 1, 2005), 3-14.
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci Number
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FORMULA
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Sequence is periodic with Pisano period 12 = (0,1,1,2,3,5,0,5,5,2,7,1).
a(n) = (1/396)*{-17*(n mod 12)+49*[(n+1) mod 12]+214*[(n+2) mod 12]-149*[(n+3) mod 12]+115*[(n+4) mod 12]+16*[(n+5) mod 12]-149*[(n+6) mod 12]+181*[(n+7) mod 12]-50*[(n+8) mod 12]-17*[(n+9) mod 12]-17*[(n+10) mod 12]+16*[(n+11) mod 12]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 24 2006
a(n) = (1/396)*{49*[n mod 12] + 214*[(n + 1) mod 12] - 149*[(n + 2) mod 12] + 115*[(n + 3) mod 12] + 16*[(n + 4) mod 12] - 149*[(n + 5) mod 12] + 181*[(n + 6) mod 12] - 50*[(n + 7) mod 12] - 17*[(n + 8) mod 12] - 17*[(n + 9) mod 12] + 16*[(n + 10) mod 12] - 17*[(n + 11) mod 12]}, with n> = 0. - Paolo P. Lava (ppl(AT)spl.at), May 30 2007
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EXAMPLE
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a(8) = F(8) mod 8 = 21 mod 8 = 5.
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MATHEMATICA
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a={}; Do[f=Fibonacci[n]; AppendTo[a, Mod[f, 8]], {n, 1, 30}]; a (Vladimir Orlovsky, Jul 23 2008)
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PROGRAM
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(PARI) for (n=0, 100, print1(fibonacci(n)%8", "))
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CROSSREFS
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Cf. A000045, A011655, A082115, A079343, A082116, A082117, A079344, A079345, A111958.
Sequence in context: A068909 A039705 A082118 this_sequence A096535 A126047 A023049
Adjacent sequences: A079341 A079342 A079343 this_sequence A079345 A079346 A079347
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jan 04 2003
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 06 2008 at the suggestion of R. J. Mathar
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