|
|
A128851
|
|
Denominators of the continued fraction convergents of the decimal concatenation of the prime-indexed primes.
|
|
1
|
|
|
1, 2, 3, 17, 20, 37, 94, 131, 225, 581, 806, 1387, 2193, 3580, 63053, 66633, 129686, 196319, 522324, 718643, 2678253, 8753402, 20185057, 69308573, 436036495, 941381563, 9849852125, 10791233688, 20641085813, 31432319501, 83505724815
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Prime-indexed primes (pips) or primeth primes 3, 5, 11, 17, 31, 41, 59, 67, ... are concatenated and then preceded by a decimal point to create the fraction N = .35111731415967... 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.
|
|
LINKS
|
|
|
PROG
|
(PARI) cattpips(n) = { a="."; forprime(x=2, n, a=concat(a, prime(x))); a=eval(a) }
cfrac2(m, f) = { default(realprecision, 1000); cf = vector(m+10); cf = contfrac(f); for(m1=1, 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", "); ) }
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|