A128873 Numerator of the continued fraction convergents of the decimal concatenation of the powers of 2.

0, 1, 84, 85, 1444, 1529, 85539, 87068, 172607, 259675, 691957, 1643589, 192991870, 194635459, 776898247, 1748431953, 9519058012, 11267489965, 99658977732, 210585445429, 8312491349463, 16835568144355, 25148059493818

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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(numer", "); numer2=numer; denom2=denom; ) }

Crossrefs

Sequence in context: A033404 A252723 A341304 * A095607 A068405 A349760

Adjacent sequences: A128870 A128871 A128872 * A128874 A128875 A128876

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 18 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved