A202154 Decimal expansion of sqrt(phi) / (1 - phi/e) where phi=(1+sqrt(5))/2.

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

Offset

1,1

Comments

Sqrt(phi) / (1 - phi/e) is somewhat close to Pi.

Because phi/e < 1 we have sqrt(phi) / (1 - phi/e) = sqrt(phi) * Sum_{n=0..Infinity}( phi/e) ^n. We obtain a better approximation of Pi with 14 terms: sqrt(phi) * Sum_{n=0..14} ( phi/e) ^n = 3.14135146821891366128707....

Links

Table of n, a(n) for n=1..105.

Example

3.14266274735970351791829....

Mathematica

RealDigits[N[Sqrt[GoldenRatio]/(1-GoldenRatio/E), 105]]

Prog

(PARI) phi=(1+sqrt(5))/2; sqrt(phi)/(1-phi/exp(1)) \\ Charles R Greathouse IV, Dec 28 2011

Crossrefs

Cf. A001113.

Sequence in context: A309650 A139432 A363653 * A115208 A234930 A351887

Adjacent sequences: A202151 A202152 A202153 * A202155 A202156 A202157

Keyword

nonn,cons

Author

Michel Lagneau, Dec 13 2011

Status

approved