This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101342 #19 Jan 05 2025 19:51:38
%S A101342 0,1,2,13,610,1346269,6557470319842,155576970220531065681649693,
%T A101342 87571595343018854458033386304178158174356588264390370,
%U A101342 27745922289305716855338470916082815029348872029647830861914852073402148308000613611082094085891168867554589
%N A101342 Fibonacci-Mersenne numbers.
%C A101342 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 A101342 J. Shallit, <a href="https://web.archive.org/web/2024*/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://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/19-1/elementary19-1.pdf">Solution</a> 19,1 Feb. (1981) 92. [_Wolfdieter Lang_, Nov 04 2010]
%F A101342 Fibonacci(Mersenne(n)) == Fibonacci(2^n-1)
%F A101342 a(n) = A088334(n-2) - 1. - _R. J. Mathar_, Apr 23 2007
%F A101342 a(n) = A000045(A000225(n)). - _Omar E. Pol_, Oct 29 2013
%o A101342 (PARI) for(x=0,10,print( fibonacci(2^x-1) ))
%Y A101342 Cf. A088334 (infinite product for 1/phi). [_Wolfdieter Lang_, Nov 04 2010]
%K A101342 nonn
%O A101342 0,3
%A A101342 _Jorge Coveiro_, Dec 24 2004