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%I #18 Jan 18 2022 10:18:01
%S 2,1,3,7,6,6,9,5,0,9,6,7,2,6,9,8,4,3,3,3,1,7,1,4,9,8,1,6,9,0,3,2,6,1,
%T 9,4,1,9,0,3,9,6,6,6,3,1,7,4,4,2,0,9,7,5,8,4,7,2,1,2,1,4,7,1,0,5,2,3,
%U 8,7,1,0,1,1,6,3,4,5,5,0,5,2,5,3,9,6,5,8,8,6,2,6,3,0,5,3,3,3,6,6,0,8,6,8,0
%N Decimal expansion of Sum_{n>=1} 1/F(n)^n, where F=A000045 (Fibonacci numbers).
%e 2.13766950967269843331714981... = 1/1^1 + 1/1^2+ 1/2^3+ 1/3^4 +1/5^5 +1/8^6 +...
%p with(combinat,fibonacci):Digits:=120:s:=sum( evalf(1/ fibonacci(n)^n),n=1..200):print(s):
%t digits = 105; NSum[1/Fibonacci[n]^n, {n, 1, Infinity}, NSumTerms -> digits, WorkingPrecision -> digits] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 21 2014 *)
%o (PARI) suminf(n=1, 1/fibonacci(n)^n); \\ _Michel Marcus_, Feb 21 2014
%Y Cf. A079586, A158933, A000045.
%K nonn,cons
%O 1,1
%A _Michel Lagneau_, Dec 03 2011
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