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Search: id:A128875
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| A128875 |
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Denominator of the continued fraction convergents of the decimal concatenation of the powers of 2. |
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+0
1
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| 1, 8, 673, 681, 11569, 12250, 685319, 697569, 1382888, 2080457, 5543802, 13168061, 1546206939, 1559375000, 6224331939, 14008038878, 76264526329, 90272565207, 798445047985, 1687162661177, 66597788833888, 134882740328953
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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The powers of 2 = 1,2,4,8,16,32,64,... are concatenated and then preceded by a decimal point to create the fraction N = .1248163264128... This number is then evaluated with n=0,m=steps to iterate,x = N, a(0)=floor(N) using the loop: do a(n)=floor(x) x=1/(x-a(n)) n=n+1 loop until n=m
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PROGRAM
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(PARI) g(n) = f="."; for(x=0, n, a=concat(f, 2^x)); f=eval(f) { default(realprecision, 1000); cf = vector(1000); cf = contfrac(f); for(m1=0, m-1, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); print1(denom", "); numer2=numer; denom2=denom; ) }
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CROSSREFS
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Sequence in context: A015106 A099126 A101180 this_sequence A037076 A116245 A071308
Adjacent sequences: A128872 A128873 A128874 this_sequence A128876 A128877 A128878
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KEYWORD
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frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Apr 18 2007
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