|
|
A128875
|
|
Denominator of the continued fraction convergents of the decimal concatenation of the powers of 2.
|
|
0
|
|
|
1, 8, 673, 681, 11569, 12250, 685319, 697569, 1382888, 2080457, 5543802, 13168061, 1546206939, 1559375000, 6224331939, 14008038878, 76264526329, 90272565207, 798445047985, 1687162661177, 66597788833888, 134882740328953
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
frac,nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|