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 A082116 Fibonacci sequence (mod 5). 10
 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, 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; text; internal format)
 OFFSET 0,4 COMMENTS This sequence contains the complete set of residues modulo 5. See A079002. - Michel Marcus, Jan 31 2020 REFERENCES S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989. See p. 88. - N. J. A. Sloane, Feb 20 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Brandon Avila and Yongyi Chen, On Moduli For Which the Lucas Numbers Contain a Complete Residue System, Fibonacci Quart. 51 (2013), no. 2, 151-152. See p. 151. S. A. Burr, On moduli for which the Fibonacci sequence contains a complete system of residues, The Fibonacci Quarterly, 9.5 (1971), 497-504. Minjia Shi, Patrick SolĂ©, The largest number of weights in cyclic codes, arXiv:1807.08418 [cs.IT], 2018. Eric Weisstein's World of Mathematics, Fibonacci Number Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1). 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, 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, Jun 30 2007 G.f.: (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), not reduced. - Hieronymus Fischer, Jun 30 2007 a(n) = A010073(n) mod 5. - Hieronymus Fischer, Jun 30 2007 G.f.  -x*(1 + x + x^2 + 2*x^3 + 3*x^6 - x^7 - 2*x^8 - x^4 + x^9 + 4*x^10 + x^11) / ( (x - 1) * (x^4 + x^3 + x^2 + x + 1) * (x^8 - x^6 + x^4 - x^2 + 1) ). - R. J. Mathar, Jul 14 2012 MATHEMATICA Table[Mod[Fibonacci[n], 5], {n, 0, 125}] (* Alonso del Arte, Jul 29 2013 *) PROG (MAGMA) [Fibonacci(n) mod 5: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014 (PARI) a(n)=fibonacci(n)%5 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000045, A011655, A082115, A079343, A082116, A082117, A079344, A079002. Sequence in context: A051933 A234963 A131900 * A079777 A224909 A227536 Adjacent sequences:  A082113 A082114 A082115 * A082117 A082118 A082119 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 03 2003 EXTENSIONS Added a(0)=0 from Vincenzo Librandi, Feb 04 2014 STATUS approved

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Last modified January 25 18:03 EST 2021. Contains 340419 sequences. (Running on oeis4.)