A253806 One half of the maximal values of the length of the period for Fibonacci numbers modulo p (A001175(p)) for primes p > 5, according to Wall's Theorems 6 and 7.

8, 5, 14, 18, 9, 24, 14, 15, 38, 20, 44, 48, 54, 29, 30, 68, 35, 74, 39, 84, 44, 98, 50, 104, 108, 54, 114, 128, 65, 138, 69, 74, 75, 158, 164, 168, 174

Offset

1,1

Links

Table of n, a(n) for n=1..37.

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

Formula

a(n) = (prime(n+3) - 1)/2 if prime(n+3) == 1 or 9 (mod 10) and a(n) = (prime(n+3) + 1) if

prime(n+3) == 3 or 7 (mod 10), n >= 1.

Example

a(1) = 8 = 7 + 1 because prime(4) = 7 == 7 (mod 10). The length of the period for 7 is 2*8 = 16 = A001175(7).
a(2) = 5 = (11 - 1)/2 because prime(4) = 11 = 1 (mod 10). The length of the period for 11 is 10 = A001175(11).

Crossrefs

Cf. A001175, A222413, A222414.

Sequence in context: A168204 A193681 A347902 * A348688 A199806 A070484

Adjacent sequences: A253803 A253804 A253805 * A253807 A253808 A253809

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 16 2015

Status

approved