login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 08:58 EST 2019. Contains 329144 sequences. (Running on oeis4.)