Googling for 1.5353705088 produces: http://linkinghub.elsevier.com/retrieve/pii/S0898122196002295 and http://books.google.be/books?id=DL5iVYNoEa0C&pg=PA559&lpg=PA559&dq=1.5353705... where we can read Steven Finch's entry: "1.5353705088... With digital search tree constants [5.14]" Since the number in question is also known to be Sum[1/(Fibonacci[2n]),{n,1,\[Infinity]}]~N~48 Out[]=1.53537050883625298502985289665159900636701159107 as discussed in http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html it would be worthwile to check if both Finch's and S. Paszkowski's references contain an as yet unknown closed form for the infinite sum. Wouter.