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 A106296 Period of the Lucas 4-step sequence A073817 mod prime(n). 3
 5, 26, 312, 342, 120, 84, 4912, 6858, 12166, 280, 61568, 1368, 240, 162800, 103822, 303480, 205378, 226980, 100254, 357910, 2664, 998720, 1157520, 9320, 368872, 1030300, 10608, 1225042, 2614040, 13874, 2048382, 4530768, 136, 772880, 3307948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is the same as the period of Fibonacci 4-step sequence (A000078) mod prime(n) except for n=103, which corresponds to the prime 563 because the discriminant of the characteristic polynomial x^4-x^3-x^2-x-1 is -563. We have a(n) < prime(n) for primes 563 and A106280. LINKS Eric Weisstein's World of Mathematics, Fibonacci n-Step FORMULA a(n) = A106295(prime(n)). MATHEMATICA n=4; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 60}] CROSSREFS Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106280 (primes p such that x^4-x^3-x^2-x-1 mod p has 4 distinct zeros). Sequence in context: A203198 A197784 A279738 * A295114 A060516 A077537 Adjacent sequences:  A106293 A106294 A106295 * A106297 A106298 A106299 KEYWORD nonn AUTHOR T. D. Noe, May 02 2005 STATUS approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)