

A180251


Decimal expansion of 6*(phi+1)/5, where phi is (1 + sqrt(5))/2.


1



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

1,1


COMMENTS

This is an approximation to Pi.
6*(phi+1)/5 is not equal to Pi, although some have claimed this (see Dudley).  Kellen Myers, Oct 04 2013


REFERENCES

Underwood Dudley, Mathematical Cranks, MAA 1992, pp. 247, 292.
Alfred S. Posamentier and Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, New York, Prometheus Books, 2007, p. 119.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Hung Viet Chu, Square the Circle in One Minute, arXiv:1908.01202 [math.GM], 2019.
Futility Closet, A Surprise Visitor


FORMULA

Limit of A022089(n+2)/A022088(n) as n approaches infinity.
6*(phi + 1)/5 = 6*phi^2/5 = 3(3 + sqrt(5))/5 = 9/5 + sqrt(9/5).  Charles R Greathouse IV, Sep 13 2013
Equals 24/(5sqrt(5))^2.  Joost Gielen, Sep 20 2013


EXAMPLE

3.141640786499873817845504201238765741264371015766915434562538347246312555382...


MATHEMATICA

RealDigits[(6/5)GoldenRatio^2, 10, 100][[1]] (* Alonso del Arte, Apr 09 2012 *)


PROG

(PARI) 3*(3+sqrt(5))/5 \\ Charles R Greathouse IV, Sep 13 2013
(Magma)(3/10)*(1 + Sqrt(5))^2 // G. C. Greubel, Jan 17 2018


CROSSREFS

Cf. A022088, A022089, A001622, A000796.
Sequence in context: A069264 A347459 A064575 * A094119 A210622 A335113
Adjacent sequences: A180248 A180249 A180250 * A180252 A180253 A180254


KEYWORD

nonn,cons


AUTHOR

Grant Garcia, Jan 16 2011


STATUS

approved



