A101342 Fibonacci-Mersenne numbers.

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

Offset: 0

Author

Jorge Coveiro, Dec 24 2004

Keywords

• nonn

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]

Links

• J. Shallit, Problem B-423, The Fibonacci Quarterly 18,1 Feb.(1980)85. Solution 19,1 Feb. (1981) 92. [_Wolfdieter Lang_, Nov 04 2010]

Crossrefs

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

Programs

PARI

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

Formula

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