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A137987 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of factorial numbers (A000142) as coefficients.

%I A137987 #15 Feb 16 2025 08:33:07
%S A137987 3,8,6,5,7,2,8,5,1,1,2,0,0,8,5,1,2,8,5,3,8,8,3,3,5,3,0,4,8,7,3,9,2,3,
%T A137987 2,6,8,0,1,1,2,7,2,9,8,5,8,9,2,7,4,6,4,6,8,8,9,2,5,2,2,1,3,4,4,0,4,1,
%U A137987 0,1,1,7,3,4,1,4,5,8,4,0,7,3,3,2,1,0,1,3,6,7,0,3,3,5,9,3,9,4,7
%N A137987 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of factorial numbers (A000142) as coefficients.
%H A137987 G. C. Greubel, <a href="/A137987/b137987.txt">Table of n, a(n) for n = 0..5000</a>
%H A137987 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A137987 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%F A137987 Equals 1/A287013. - _Amiram Eldar_, Nov 19 2020
%p A137987 P:=proc(n) local a,i,k; a:=0; k:=1; for i from 0 by 1 to n do k:=k*i!; a:=a+1/k; print(evalf(1/a,100)); od; end: P(100);
%t A137987 RealDigits[N[(1/Sum[Product[1/((k - 1)!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* _G. C. Greubel_, Jan 02 2017 *)
%Y A137987 Cf. A000142, A137986, A137988, A137989, A287013.
%K A137987 easy,nonn,cons
%O A137987 0,1
%A A137987 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008, Apr 18 2008