A086788 Primes found among the denominators of the continued fraction rational approximations to Pi.

7, 113, 265381, 842468587426513207

Offset

1,1

Comments

The next term is too large to include.

Links

Joerg Arndt, Table of n, a(n) for n = 1..10

Cino Hilliard, Continued fractions rational approximation of numeric constants. [needs login]

Example

The first 5 rational approximations to Pi are 3/1, 22/7, 333/106, 355/113, 103993/33102; of these, the prime denominators are 7 and 113.

Prog

(PARI)
cfracdenomprime(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(denom), print1(denom, ", ")); ) }
(PARI)
default(realprecision, 10^5);
cf=contfrac(Pi);
n=0;
{ for(k=1, #cf,  \\ generate b-file
    pq = contfracpnqn( vector(k, j, cf[j]) );
    p = pq[1, 1];  q = pq[2, 1];
\\    if ( ispseudoprime(p), n+=1; print(n, " ", p) );  \\ A086785
    if ( ispseudoprime(q), n+=1; print(n, " ", q) );  \\ A086788
); }
/* Joerg Arndt, Apr 21 2013 */

Crossrefs

Cf. A086791, A086785.

Sequence in context: A371328 A159552 A228929 * A199672 A240288 A220343

Adjacent sequences: A086785 A086786 A086787 * A086789 A086790 A086791

Keyword

easy,nonn

Author

Cino Hilliard, Aug 04 2003; corrected Jul 30 2004

Extensions

Offset corrected by Joerg Arndt, Apr 21 2013

Status

approved