0,1

The numbers listed are primes. For m <= 10000 the only occurrence where both numerator and denominator are prime is 833719/265381.

Cino Hilliard, Continued fractions rational approximation of numeric constants.

The first 4 rational approximations to Pi are 3/1, 22/7, 333/106, 355/113, 103993/33102 where 3 and 103993 are primes.

(PARI) \Continued fraction rational approximation of numeric functions cfrac(m, f) = x=f; for(n=0, m, i=floor(x); x=1/(x-i); print1(i, ", ")) cfracnumprime(m, f) = { cf = vector(100000); 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(isprime(numer), print1(numer, ", ")); ) }

Sequence in context: A086829 A115976 A119119 this_sequence A116536 A003544 A137131

Adjacent sequences: A086782 A086783 A086784 this_sequence A086786 A086787 A086788

easy,nonn

Cino Hilliard (hillcino368(AT)gmail.com), Aug 04 2003