1,1

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 -> 41/19 -> ... where the numerators are A001333. - R. J. Mathar, Aug 18 2008

Is this sequence infinite?

Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.

Given c(0)=1, b(0)=1 then for i=1, 2, .. c(i)/b(i) = (c(i-1)+2*b(i-1)) /(c(i-1) + b(i-1)).

(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+.) }

Cf. A086383.

Sequence in context: A089742 A131721 A058351 this_sequence A020730 A003440 A102071

Adjacent sequences: A086392 A086393 A086394 this_sequence A086396 A086397 A086398

nonn

Cino Hilliard (hillcino368(AT)gmail.com), Sep 06 2003, Jul 30 2004, Oct 02 2005

Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at the suggestion of R. J. Mathar