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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
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
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/(5-sqrt(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
KEYWORD
nonn,cons
AUTHOR
Grant Garcia, Jan 16 2011
STATUS
approved