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A137991 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of Fibonacci numbers (A000045) as coefficients.

%I A137991 #16 Feb 16 2025 08:33:07
%S A137991 3,6,9,7,5,3,7,1,7,1,4,8,0,8,9,0,9,6,5,4,5,2,9,4,7,8,8,9,3,2,9,1,2,0,
%T A137991 8,6,2,0,4,7,6,0,7,3,5,8,0,7,6,3,4,9,4,9,9,5,7,3,5,9,7,2,8,4,6,8,6,5,
%U A137991 2,8,4,0,3,4,5,3,1,9,2,8,6,0,7,7,2,3,9,7,5,1,0,0,3,0,0,7,2,6,8
%N A137991 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of Fibonacci numbers (A000045) as coefficients.
%H A137991 G. C. Greubel, <a href="/A137991/b137991.txt">Table of n, a(n) for n = 0..2500</a>
%H A137991 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A137991 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%p A137991 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/k; print(evalf(1/a,100)); od; end: P(100);
%t A137991 RealDigits[N[1/(Sum[Product[1/Fibonacci[k], {k, 1, n}], {n, 1, 1000}]),
%t A137991 100]][[1]] (* _G. C. Greubel_, Dec 26 2016 *)
%Y A137991 Cf. A000045, A101689 (reciprocal), A137987.
%K A137991 easy,nonn,cons
%O A137991 0,1
%A A137991 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008