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A202154 Decimal expansion of sqrt(phi) / (1 - phi/e) where phi=(1+sqrt(5))/2. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A309636 A309650 A139432 * A115208 A234930 A351887

Adjacent sequences:  A202151 A202152 A202153 * A202155 A202156 A202157

KEYWORD

nonn,cons

AUTHOR

Michel Lagneau, Dec 13 2011

STATUS

approved

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Last modified August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)