A114842 Indices of Fibonacci numbers with 2 distinct prime factors.

8, 9, 10, 12, 14, 19, 22, 25, 26, 31, 34, 41, 53, 59, 61, 71, 73, 79, 89, 94, 101, 107, 109, 113, 121, 127, 151, 167, 173, 191, 193, 199, 227, 251, 271, 277, 293, 331, 353, 397, 401, 467, 587, 599, 601, 613, 631, 653, 743, 991, 1091, 1223, 1373

Offset: 1

Author

Shyam Sunder Gupta, Feb 19 2006

Keywords

• hard
• more
• nonn

Comments

A072381 is subsequence, since the only square Fibonacci numbers are 1 and 144 which are not squares of primes. - Charles R Greathouse IV, Sep 24 2012

Examples

			a(1) = 8 because 8th Fibonacci number consists of 2 distinct prime factors (i.e. 21 = 3*7).
25 is in the sequence because Fibonacci(25) = 75025 = 5^2 * 3001 consists of 2 distinct prime factors.
		

Links

• Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek, On Fibonacci numbers with few prime divisors, Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 2 (2005), 17-20.

Crossrefs

Cf. A114823-A114826, A114836-A114841.

Column k=2 of A303217.

Programs

PARI

n=1;while(n<355,if(omega(fibonacci(n))==2,print1(n,", "));n++)

Extensions

a(40)-a(50) from Donovan Johnson, Sep 27 2008

a(51)-a(52) from Max Alekseyev, Aug 18 2013

a(53) from Amiram Eldar, Oct 14 2019