A373507 Decimal expansion of 1/2 - sqrt(3)*Pi/18.
1, 9, 7, 7, 0, 0, 1, 0, 5, 9, 6, 0, 9, 6, 3, 6, 9, 1, 5, 6, 7, 6, 5, 3, 6, 2, 3, 7, 2, 6, 3, 0, 7, 3, 7, 7, 9, 5, 2, 6, 5, 5, 6, 2, 5, 3, 1, 7, 8, 7, 6, 5, 7, 0, 7, 3, 8, 3, 5, 2, 5, 1, 0, 7, 6, 8, 6, 4, 6, 1, 3, 6, 4, 7, 8, 9, 4, 1, 0, 1, 9, 3, 8, 5, 9, 7
Offset: 0
Examples
0.1977001059609636915676536237263...
Links
- Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27.
Programs
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Maple
1/2-sqrt(3)*Pi/18; evalf(%) ;
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Mathematica
RealDigits[1/2 - Sqrt[3]*Pi/18, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)
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PARI
1/2 - sqrt(3)*Pi/18 \\ Amiram Eldar, Jun 10 2024
Formula
Equals Sum_{n>=2} 1/((n-1)*binomial(2n,n)).
Sum_{n>=2} (-1)^n/((n-1)*binomial(2n,n)) = 3*log(phi)/sqrt(5) - 1/2 = 0.145613... where phi is the golden ratio.