A106296 Period of the Lucas 4-step sequence A073817 mod prime(n).

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

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

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number

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), A106295.

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