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A135598 Decimal expansion of the number whose Pierce expansion has the sequence of Fibonacci numbers (A000045) as coefficients.

%I A135598 #12 Feb 16 2025 08:33:07
%S A135598 3,6,2,8,0,5,6,9,1,1,3,2,0,5,6,3,5,5,2,9,1,0,5,5,1,5,8,6,1,2,3,8,0,8,
%T A135598 9,8,2,8,8,5,1,6,5,3,9,2,3,3,9,6,2,0,7,4,0,4,7,5,3,2,7,1,4,8,4,2,4,7,
%U A135598 6,2,3,6,3,8,4,6,8,7,0,2,3,6,1,4,4,1,4,9,2,1,2,9,5,8,6,3,6,5,7
%N A135598 Decimal expansion of the number whose Pierce expansion has the sequence of Fibonacci numbers (A000045) as coefficients.
%H A135598 G. C. Greubel, <a href="/A135598/b135598.txt">Table of n, a(n) for n = 0..2500</a>
%H A135598 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A135598 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%p A135598 with (combinat,fibonacci); P:=proc(n) local a,i,k; a:=0; k:=1; for i from 1 by 1 to n do k:=k*fibonacci(i); a:=a-(-1)^i/k; print(evalf(a,100)); od; end: P(100);
%t A135598 RealDigits[N[(Sum[(-1)^n*Product[1/Fibonacci[k], {k, 1, n}], {n, 1, 100}]), 50]][[1]] (* _G. C. Greubel_, Dec 26 2016 *)
%Y A135598 Cf. A000045, A137991.
%K A135598 easy,nonn,cons
%O A135598 0,1
%A A135598 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008