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 A091668 Decimal expansion of exp(2*Pi/v) * (v/(1+(5^(3/4)/((1+v)/2)^(5/2)-1)^(1/5))-(1+v)/2), where v = sqrt(5). 1
 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; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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(-2*Pi*sqrt(5)). - Michael Somos, Sep 12 2005 REFERENCES 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. LINKS 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 FORMULA Equals 1/A091900. EXAMPLE 0.999999208... PROG (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 */ CROSSREFS Sequence in context: A346435 A346449 A290665 * A196498 A277535 A292905 Adjacent sequences:  A091665 A091666 A091667 * A091669 A091670 A091671 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jan 27 2004 STATUS approved

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Last modified September 18 12:35 EDT 2021. Contains 347527 sequences. (Running on oeis4.)