OFFSET
4,7
COMMENTS
Wall (1960) in Theorems 6 and 7 proved that a(n) is an integer for n >= 4. Jarden (1946) proved that the sequence is unbounded. See Elsenhans and Jahnel (2010), pp. 1-2.
LINKS
A. Elsenhans and J. Jahnel, The Fibonacci sequence modulo p^2 -- An investigation by computer for p < 10^14, arXiv 1006.0824 [math.NT], 2010.
D. Jarden, Two theorems on Fibonacci's sequence, Amer. Math. Monthly, 53 (1946), 425-427.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.
Wikipedia, Wall-Sun-Sun prime
FORMULA
MATHEMATICA
With[{p = Prime[n]}, T = Table[a = {1, 0}; a0 = a; k = 0; While[k++; s = Mod[Plus @@ a, p]; a = RotateLeft[a]; a[[2]] = s; a != a0]; k, {n, 1, 130}]; Table[L = KroneckerSymbol[p, 5]; (3 - L)/2 (p - L)/T[[n]], {n, 4, 130}]] (* after T. D. Noe *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Dec 09 2017
STATUS
approved