A178762 Prime numbers that are Fibonacci integers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 61, 89, 107, 199, 211, 233, 281, 421, 521, 1103, 1597, 2161, 2207, 2521, 3001, 3571, 5779, 9349, 9901, 14503, 19801, 28657, 90481, 103681, 109441, 135721, 141961, 514229, 3010349, 6376021, 11128427

Offset

1,1

Comments

A Fibonacci integer is a number that can be written as the product and/or quotient of Fibonacci numbers (A000045). For example, 107 is a Fibonacci integer because Fib(36)/(Fib(18)*Fib(3)*Fib(4)^3) = 107. Observe that the prime Fibonacci numbers (A005478) are a subset of these primes. Luca, Pomerance, and Wagner conjecture that this sequence is infinite. The paper's Remark 2 and sequences A152012, A178763, and A178764 are useful in finding these primes.

Links

Table of n, a(n) for n=1..44.

Florian Luca, Carl Pomerance, and Stephan Wagner, Fibonacci Integers (preprint)

Crossrefs

Sequence in context: A299171 A347977 A002267 * A051750 A268109 A283225

Adjacent sequences: A178759 A178760 A178761 * A178763 A178764 A178765

Keyword

nonn

Author

T. D. Noe, Jun 10 2010

Status

approved