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 A086788 Primes found among the denominators of the continued fraction rational approximations to Pi. 3
 7, 113, 265381, 842468587426513207 (list; graph; refs; listen; history; text; internal format)
 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: A064330 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

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Last modified October 25 18:25 EDT 2020. Contains 338012 sequences. (Running on oeis4.)