A201615 Decimal expansion of Sum_{n>=1} 1/F(n)^n, where F=A000045 (Fibonacci numbers).

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, 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, 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

Offset: 1

Author

Michel Lagneau, Dec 03 2011

Keywords

• nonn
• cons

Examples

			2.13766950967269843331714981... = 1/1^1 + 1/1^2+ 1/2^3+ 1/3^4 +1/5^5 +1/8^6 +...
		

Crossrefs

Cf. A079586, A158933, A000045.

Programs

Maple

with(combinat,fibonacci):Digits:=120:s:=sum( evalf(1/ fibonacci(n)^n),n=1..200):print(s):

Mathematica

digits = 105; NSum[1/Fibonacci[n]^n, {n, 1, Infinity}, NSumTerms -> digits, WorkingPrecision -> digits] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 21 2014 *)

PARI

suminf(n=1, 1/fibonacci(n)^n); \\ Michel Marcus, Feb 21 2014