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A086788
Primes found among the denominators of the continued fraction rational approximations to Pi.
3
7, 113, 265381, 842468587426513207
OFFSET
1,1
COMMENTS
The next term is too large to include.
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
Sequence in context: A371328 A159552 A228929 * A199672 A240288 A220343
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Aug 04 2003; corrected Jul 30 2004
EXTENSIONS
Offset corrected by Joerg Arndt, Apr 21 2013
STATUS
approved