OFFSET
1,1
COMMENTS
Or, starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and twice bottom to get the new top. Or, A001333(n) is prime.
The transformation of fractions is 1/1 -> 3/2 -> 7/5 -> 17/12 -> 41/29 -> ... A001333(n)/A000129(n). - R. J. Mathar, Aug 18 2008
Is this sequence infinite?
REFERENCES
Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..18
FORMULA
MATHEMATICA
Select[Numerator[Convergents[Sqrt[2], 250]], PrimeQ] (* Harvey P. Dale, Oct 19 2011 *)
PROG
(PARI) \Continued fraction rational approximation of numeric constants f. m=steps. cfracnumprime(m, f) = { default(realprecision, 3000); cf = vector(m+10); x=f; for(n=0, m, i=floor(x); x=1/(x-i); cf[n+1] = i; ); for(m1=0, m, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); if(ispseudoprime(numer), print1(numer, ", ")); ) }
(PARI) primenum(n, k, typ) = \yp = 1 num, 2 denom. print only prime num or denom. { local(a, b, x, tmp, v); a=1; b=1; for(x=1, n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1, v=a, v=b); if(isprime(v), print1(v", "); ) ); print(); print(a/b+.) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Sep 06 2003, Jul 30 2004, Oct 02 2005
EXTENSIONS
Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar
STATUS
approved