1,1

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 (alex(AT)kolmogorov.com), Aug 09 2006

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 (alex(AT)kolmogorov.com), Aug 09 2006

Composites and Primes Among Powers of Fibonacci Numbers increased or decreased by one V E Hoggatt Jr and M Bicknell-Johnson, Fibonacci Quarterly vol. 15 (1977), page 2.

Greatest Common Divisors in Altered Fibonacci Sequences U Dudley, B Tucker Fibonacci Quarterly 1971, pages 89-91.

Letter from Toby Gee in Mathematical Spectrum, vol. 29 (1996/1997), page 68.

R. Knott, The Mathematical Magic of the Fibonacci Numbers.

a(5) = 1336337 because 1336337 is prime,

and 1336337-1 = 1336336 = 34^4+1 = Fibonacci(9)^4+1

Select[Take[Intersection[Flatten[Table[Fibonacci[3n]^(2^m)+1, {n, 1, 300}, {m, 1, 7}]]], {1, 400}], PrimeQ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 09 2006

Cf. A005478, A001605, A000045.

Adjacent sequences: A093425 A093426 A093427 this_sequence A093429 A093430 A093431

Sequence in context: A086362 A089894 A077718 this_sequence A081479 A096996 A070294

nonn

Lior Manor (lior.manor(AT)gmail.com) May 12 2004

More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 09 2006