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
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