A307086 Decimal expansion of 4*(5 - sqrt(5)*log(phi))/25, where phi is the golden ratio (A001622).

6, 2, 7, 8, 3, 6, 4, 2, 3, 6, 1, 4, 3, 9, 8, 3, 8, 4, 4, 4, 4, 2, 2, 6, 7, 0, 6, 8, 1, 9, 7, 5, 7, 8, 2, 9, 8, 3, 0, 1, 7, 1, 7, 2, 6, 9, 8, 3, 8, 8, 4, 1, 3, 8, 0, 9, 7, 1, 9, 7, 5, 5, 8, 4, 0, 2, 9, 7, 5, 5, 1, 3, 8, 1, 5, 5, 4, 7, 2, 1, 5, 4, 5, 5, 4, 0, 3, 8, 9, 4, 1, 2, 1, 1, 1, 2, 0, 1, 7, 8, 3, 7, 4, 6, 7, 7, 8, 2, 8, 8, 6, 7, 0, 2, 9, 3, 8, 5, 7, 4

Offset

0,1

Comments

Decimal expansion of the alternating sum of the reciprocals of the central binomial coefficients (A000984).

Links

Table of n, a(n) for n=0..119.

Eric Weisstein's World of Mathematics, Central Binomial Coefficient

Index entries for transcendental numbers

Formula

Equals Sum_{k>=0} (-1)^k/binomial(2*k,k).

Equals Sum_{k>=0} (-1)^k*(k!)^2/(2*k)!.

Example

1/1 - 1/2 + 1/6 - 1/20 + 1/70 - 1/252 + ... = 0.62783642361439838444422670681975782983017172698388...

Mathematica

RealDigits[4 (5 - Sqrt[5] Log[GoldenRatio])/25, 10, 120][[1]]

Prog

(PARI) 4*(5 - sqrt(5)*log((sqrt(5)+1)/2))/25 \\ Charles R Greathouse IV, May 15 2019

Crossrefs

Cf. A000984, A001622, A073016, A086465, A091682, A145433, A145434.

Sequence in context: A163340 A326823 A244381 * A021090 A368669 A270138

Adjacent sequences: A307083 A307084 A307085 * A307087 A307088 A307089

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Mar 23 2019

Status

approved