OFFSET
1,1
COMMENTS
Let a(n) = Fibonacci(x)^y+1, then there exists some a,b > 0, such that x = 3*a and y = 2^b. For the example a(5) = 1336337: x = 9, y = 4, a = 3 and b = 2.
Last digit seems to be usually 7, except for a(1) and a(6). - Alexander Adamchuk, Aug 09 2006
LINKS
U. Dudley, B. Tucker, Greatest Common Divisors in Altered Fibonacci Sequences, Fibonacci Quarterly 1971, pages 89-91.
Letter from Toby Gee in Mathematical Spectrum, Fibonacci numbers, vol. 29 (1996/1997), page 66.
V. E. Hoggatt Jr. and M. Bicknell-Johnson, Composites and Primes Among Powers of Fibonacci Numbers increased or decreased by one, Fibonacci Quarterly vol. 15 (1977), page 2.
Ron Knott, The Mathematical Magic of the Fibonacci Numbers.
EXAMPLE
a(5) = 1336337 because 1336337 is prime, and 1336337-1 = 1336336 = 34^4+1 = Fibonacci(9)^4+1.
a(6) = Fibonacci(15)^8 + 1, a(7) = Fibonacci(48)^8 + 1, a(8) = Fibonacci(51)^8 + 1, a(9) = Fibonacci(63)^8 + 1, a(10) = Fibonacci(21)^32 + 1, a(11) = Fibonacci(198)^4 + 1, a(12) = Fibonacci(204)^8 + 1, a(13) = Fibonacci(366)^8 + 1. - Alexander Adamchuk, Aug 09 2006
MATHEMATICA
Select[Take[Intersection[Flatten[Table[Fibonacci[3n]^(2^m)+1, {n, 1, 300}, {m, 1, 7}]]], {1, 400}], PrimeQ] (* Alexander Adamchuk, Aug 09 2006 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Lior Manor, May 12 2004
EXTENSIONS
More terms from Alexander Adamchuk, Aug 09 2006
STATUS
approved