A128875 Denominator of the continued fraction convergents of the decimal concatenation of the powers of 2.

1, 8, 673, 681, 11569, 12250, 685319, 697569, 1382888, 2080457, 5543802, 13168061, 1546206939, 1559375000, 6224331939, 14008038878, 76264526329, 90272565207, 798445047985, 1687162661177, 66597788833888, 134882740328953

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

(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; ) }

Crossrefs

Sequence in context: A172919 A286394 A101180 * A199801 A278857 A334088

Adjacent sequences: A128872 A128873 A128874 * A128876 A128877 A128878

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 18 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved