A181393 Numbers of the form Fibonacci(2^c)/Fibonacci(2^b), 1 <= b < c.

3, 7, 21, 47, 329, 987, 2207, 103729, 726103, 2178309, 4870847, 10749959329, 505248088463, 3536736619241, 10610209857723, 23725150497407, 115561578124843393729, 255044402921529369959903, 11987086937311880388115441, 83909608561183162716808087, 251728825683549488150424261

Offset: 1

Author

Vladimir Shevelev, Oct 17 2010

Keywords

• nonn

Comments

Using an Eratosthenes-like sieve, we find "primes" of the form P_k = Fibonacci(2^(k+1)) / Fibonacci(2^k) = A001566(k-1), k=1,2,..., such that every term has a unique "prime" factorization.

Examples

			If k=3, m=1, by the latter formula, we have a(8) = A001566(2)*A001566(3) = 47*2207 = 103729.
		

Crossrefs

Cf. A000045, A001566.

Formula

For n >= 1, a((n^2-n+2)/2) = P_n = A001566(n-1); for 1 <= m < k, a((k^2+3*k)/2-m) = Product_{i=m+1..k} A001566(i).

Extensions

a(12)-a(16) corrected and more terms from Jason Yuen, Feb 10 2025