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Search: id:A091667
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| A091667 |
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Decimal expansion of ((-1-Sqrt[5])/2+Sqrt[(5+Sqrt[5])/2])*E^((2*Pi)/5). |
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2
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| 9, 9, 8, 1, 3, 6, 0, 4, 4, 5, 9, 8, 5, 0, 9, 3, 3, 2, 1, 5, 0, 0, 2, 4, 4, 5, 9, 0, 4, 7, 0, 7, 4, 7, 3, 5, 3, 1, 1, 3, 8, 2, 9, 9, 4, 7, 6, 3, 0, 4, 3, 9, 8, 2, 1, 8, 5, 5, 8, 3, 8, 7, 4, 0, 7, 0, 3, 5, 0, 3, 2, 4, 6, 8, 9, 4, 6, 4, 4, 1, 3, 3, 5, 7, 7, 1, 7, 7, 2, 7, 0, 8, 6, 7, 5, 0, 5, 8, 2, 6, 1, 7, 9, 4, 8
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Has a nice (non-simple) continued fraction due to Ramanujan.
Continued fraction is 1/(1+q/(1+q^2/(1+q^3/(1+...)))) where q=exp(-2pi). - Michael Somos Sep 12 2005
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REFERENCES
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K. S. Rao, Ramanujan, a Mathematical Genius, pp. 42 Eastwest Books, Chennai Madras 2000.
B. C. Berndt & R. A. Rankin, Ramanujan: Letters And Commentary, pp. 29 AMS Providence RI 1995.
B. C. Berndt & R. A. Rankin, Ramanujan: Essays And Surveys, pp. 243 AMS Providence RI 2001.
G. H. Hardy, Ramanujan: Twelve Lectures on subjects as suggested by his Life and Work, pp. 8 section (1.11), AMS Chelsea Providence RI 1999.
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LINKS
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Eric Weisstein's World of Mathematics, Ramanujan Continued Fractions
H. Gierhardts, Three Famous Formulas Of Ramamanujan
S. Ramanujan, Journal of the Indian Mathematical Society, Question 352(iv, 40)
Wikipedia, Ramanujan's continued fractions
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EXAMPLE
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0.998136044...
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PROGRAM
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(PARI) {a(n)=x=exp(2/5*Pi)*(sqrt((5+sqrt(5))/2)-(1+sqrt(5))/2); floor(x*10^(n+1))%10} /* Michael Somos Sep 12 2005 */
(PARI) {a(n)= x=exp(-2*Pi); x=contfracpnqn(matrix(2, oo, i, j, if(j==1, i==1, if(i==1, x, 1)^(j-2)))); x=t[1, 1]/t[2, 1]; floor(x*10^(n+1))%10} /* Michael Somos Sep 12 2005 */
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CROSSREFS
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Equals 1/A091899.
Sequence in context: A072908 A019895 A144669 this_sequence A051554 A146493 A019896
Adjacent sequences: A091664 A091665 A091666 this_sequence A091668 A091669 A091670
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KEYWORD
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nonn,cons
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jan 27, 2004
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