S000472


Primes p producing the longest possible period in the Fibonacci 3-step (mod p) sequence.

3, 5, 23, 59, 71, 89, 113, 137, 179, 191, 251, 317, 353, 383, 389, 443, 449, 467, 509, 521, 641, 647, 719, 797, 839, 881, 947, 971, 983, 1013, 1049, 1061, 1103, 1193, 1259, 1277, 1301, 1373, 1409, 1499, 1511, 1523, 1607, 1637, 1709, 1721, 1787, 1901, 1973

1

S000472

Using the 1000 terms given in the b-file for A106302, we select the primes p producing the longest period, which is p^2 + p + 1.

T. D. Noe, Plot of 163 terms

T. D. Noe, Table of 163 terms

Eric W. Weisstein, MathWorld: Fibonacci n-Step Number

(Mma) (* numbers in s from b106302 *) t3 = Table[IntegerDigits[s[[i]], Prime[i]], {i, Length[s]}]; Flatten[Prime[Position[t3, {1, 1, 1}]]]

Cf. A106302.

nonn

T. D. Noe, Feb 10 2015

© Tony D Noe 2014-2015