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A106281 Primes p such that the polynomial x^5-x^4-x^3-x^2-x-1 mod p has 5 distinct zeros. 4
691, 733, 3163, 4259, 4397, 5419, 6637, 6733, 8009, 8311, 9803, 11731, 14923, 17291, 20627, 20873, 22777, 25111, 26339, 27947, 29339, 29389, 29527, 29917, 34123, 34421, 34739, 34757, 36527, 36809, 38783, 40433, 40531, 41131, 42859, 43049 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This polynomial is the characteristic polynomial of the Fibonacci and Lucas 5-step sequences, A001591 and A074048. The periods of the sequences A001591(k) mod p and A074048(k) mod p have length less than p.

LINKS

Table of n, a(n) for n=1..36.

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

MATHEMATICA

t=Table[p=Prime[n]; cnt=0; Do[If[Mod[x^5-x^4-x^3-x^2-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 5000}]; Prime[Flatten[Position[t, 5]]]

CROSSREFS

Cf. A106278 (number of distinct zeros of x^5-x^4-x^3-x^2-x-1 mod prime(n)), A106298, A106304 (period of Lucas and Fibonacci 5-step mod prime(n)).

Sequence in context: A029825 A180320 A159283 * A127341 A135316 A160500

Adjacent sequences:  A106278 A106279 A106280 * A106282 A106283 A106284

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)