A101342 Fibonacci-Mersenne numbers: a(n) = Fibonacci(2^n-1).

0, 1, 2, 13, 610, 1346269, 6557470319842, 155576970220531065681649693, 87571595343018854458033386304178158174356588264390370, 27745922289305716855338470916082815029348872029647830861914852073402148308000613611082094085891168867554589

Offset

0,3

Comments

Product_{n >= 1} 1+1/a(n+1) = (1+sqrt(5))/2 (golden section phi, tau or alpha). See the Shallit reference. [Wolfdieter Lang, Nov 04 2010]

This is a strong divisibility sequence, that is, gcd(a(n), a(m)) = a(gcd(n, m)) for n, m >= 1. In particular, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, Jul 05 2026

Links

Table of n, a(n) for n=0..9.

Jeffrey Shallit, Problem B-423, The Fibonacci Quarterly 18,1 Feb.(1980)85; Solution 19,1 Feb. (1981) 92. [Wolfdieter Lang, Nov 04 2010]

Formula

a(n) = Fibonacci(Mersenne(n)) = Fibonacci(2^n-1).

a(n) = A088334(n-2) - 1. - R. J. Mathar, Apr 23 2007

a(n) = A000045(A000225(n)). - Omar E. Pol, Oct 29 2013

Prog

(PARI) for(x=0, 10, print( fibonacci(2^x-1) ))

Crossrefs

Cf. A088334 (infinite product for 1/phi). [Wolfdieter Lang, Nov 04 2010]

Cf. A000045, A000225.

Sequence in context: A154356 A013111 A179434 * A119122 A109947 A175513

Adjacent sequences: A101339 A101340 A101341 * A101343 A101344 A101345

Keyword

nonn,easy

Author

Jorge Coveiro, Dec 24 2004

Status

approved