A101342 - OEIS

%I #18 Jan 22 2019 14:23:08

%S 0,1,2,13,610,1346269,6557470319842,155576970220531065681649693,

%T 87571595343018854458033386304178158174356588264390370,

%U 27745922289305716855338470916082815029348872029647830861914852073402148308000613611082094085891168867554589

%N Fibonacci-Mersenne numbers.

%C 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]

%H J. Shallit, <a href="https://www.fq.math.ca/Scanned/18-1/elementary18-1.pdf">Problem B-423</a>, The Fibonacci Quarterly 18,1 Feb.(1980)85. <a href="https://www.fq.math.ca/Scanned/19-1/elementary19-1.pdf">Solution</a> 19,1 Feb. (1981) 92. [_Wolfdieter Lang_, Nov 04 2010]

%F Fibonacci(Mersenne(n)) == Fibonacci(2^n-1)

%F a(n) = A088334(n-2) - 1. - _R. J. Mathar_, Apr 23 2007

%F a(n) = A000045(A000225(n)). - _Omar E. Pol_, Oct 29 2013

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

%Y Cf. A088334 (infinite product for 1/phi). [_Wolfdieter Lang_, Nov 04 2010]

%K nonn

%O 0,3

%A _Jorge Coveiro_, Dec 24 2004