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A082116
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Fibonacci sequence (mod 5).
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6
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1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Eric Weisstein's World of Mathematics, Fibonacci Number
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FORMULA
| Sequence is periodic with Pisano period 20.
a(n)=1/380*{ - 15*(n mod 20) + 23*[(n + 1) mod 20] + 61*[(n + 2) mod 20] - 34*[(n + 3) mod 20] + 4*[(n + 4) mod 20] - 34*[(n + 5) mod 20] + 42*[(n + 6) mod 20] + 23*[(n + 7) mod 20] + 23*[(n + 8) mod 20] + 4*[(n + 9) mod 20] - 72*[(n + 10) mod 20] + 80*[(n + 11) mod 20] - 53*[(n + 12) mod 20] + 42*[(n + 13) mod 20] + 4*[(n + 14) mod 20] - 53*[(n + 15) mod 20] + 61*[(n + 16) mod 20] - 15*[(n + 17) mod 20] - 15*[(n + 18) mod 20] + 4*[(n + 19) mod 20]} with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Dec 20 2006
a(n)=2+((n mod 20)-((n-1)mod 20)-((n-3)mod 20)-((n-4)mod 20)+3*((n-5)mod 20)-3*((n-6)mod 20)+2*((n-8)mod 20)-3*((n-9)mod 20)+4*((n-10)mod 20)-4*((n-11)mod 20)+((n-13)mod 20)+((n-14)mod 20)+2*((n-15)mod 20)-2*((n-16)mod 20)-2*((n-18)mod 20)+3*((n-19)mod 20))/20. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 30 2007
G.f.: g(x)=(x+x^2+2x^3+3x^4+3x^6+3x^7+x^8+4x^9+4x^11+4x^12+3x^13+2x^14+2x^16+= 2x^17+4x^18+x^19)/(1-x^20). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 30 2007
a(n)=A010073(n) mod 5. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 30 2007
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MATHEMATICA
| f[n_]:=Mod[Fibonacci[n], 5]; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 18 2010]
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CROSSREFS
| Cf. A011655, A082115, A079343, A082116, A082117, A079344, A079344.
Sequence in context: A193682 A051933 A131900 * A079777 A047773 A187988
Adjacent sequences: A082113 A082114 A082115 * A082117 A082118 A082119
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 03, 2003
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