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Search: id:A091668
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| A091668 |
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Decimal expansion of ((-1-Sqrt[5])/2+Sqrt[5]/(1+(-1+(5^(3/4)*(-1+Sqrt[5])^(5/2))/(4*Sqrt[2]))^(1/5)))*E^((2*Pi)/Sqrt[5]). |
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2
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| 9, 9, 9, 9, 9, 9, 2, 0, 8, 7, 3, 2, 9, 0, 0, 7, 9, 3, 1, 2, 7, 4, 7, 3, 0, 4, 0, 9, 3, 3, 7, 1, 5, 7, 8, 6, 5, 1, 5, 1, 5, 9, 4, 1, 5, 0, 0, 5, 4, 0, 9, 4, 7, 8, 9, 4, 4, 7, 8, 4, 1, 2, 5, 3, 6, 9, 9, 2, 1, 5, 6, 7, 5, 7, 8, 5, 0, 4, 2, 0, 6, 3, 9, 3, 3, 5, 7, 4, 4, 3, 0, 4, 8, 1, 1, 0, 7, 9, 9, 3, 8, 4, 8, 8, 7
(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*sqrt(5)). - Michael Somos Sep 12 2005
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REFERENCES
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K. S. Rao, Srinivasa Ramanujan, a Mathematical Genius, pp. 42, Eastwest Books Chennai Madras 2000.
G. H. Hardy, Ramanujan: Twelve Lectures on subjects as suggested by his Life and Work, pp. 8 section (1.12), AMS Chelsea Providence RI 1999.
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LINKS
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I. E. S. Cartuja, Srinivasa Ramanujan(Text in Spanish)
H. Gierhardts, Three Famous Formulas Of Ramanujan
S. Sarvotham, Ramanujan
Eric Weisstein's World of Mathematics, Ramanujan Continued Fractions
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EXAMPLE
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0.999999208...
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PROGRAM
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(PARI) {a(n)=local(s); s=sqrt(5); x=exp(2*Pi/s)*(s/(1+(5^(3/4)/((1+s)/2)^(5/2)-1)^(1/5))-(1+s)/2); floor(x*10^(n+1))%10} /* Michael Somos Sep 12 2005 */
(PARI) {a(n)= x=exp(-2*Pi*sqrt(5)); 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/A091900.
Sequence in context: A093409 A111692 A100547 this_sequence A116667 A137577 A099646
Adjacent sequences: A091665 A091666 A091667 this_sequence A091669 A091670 A091671
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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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