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

1,1

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

Links

Table of n, a(n) for n=1..53.

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.

Example

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.

Prog

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

Crossrefs

Cf. A114823-A114826, A114836-A114841.

Column k=2 of A303217.

Sequence in context: A054011 A280946 A209724 * A169928 A067683 A338026

Adjacent sequences: A114839 A114840 A114841 * A114843 A114844 A114845

Keyword

hard,more,nonn

Author

Shyam Sunder Gupta, Feb 19 2006

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

Status

approved