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 A086791 Primes found among the numerators of the continued fraction rational approximations to e. 3
 2, 3, 11, 19, 193, 49171, 1084483, 563501581931, 332993721039856822081, 3883282200001578119609988529770479452142437123001916048102414513139044082579 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Joerg Arndt, Table of n, a(n) for n = 1..11 Cino Hilliard, Continued fractions rational approximation of numeric constants. [needs login] EXAMPLE The first 8 rational approximations to e are 2/1, 3/1, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71. The numerators 2, 3, 11, 19, 193 are primes. PROG (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) default(realprecision, 10^5); cf=contfrac(exp(1)); 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) );  \\ A086791 \\    if ( ispseudoprime(q), n+=1; print(n, " ", q) );  \\ A094008 ); } /* Joerg Arndt, Apr 21 2013 */ CROSSREFS Cf. A086788. Sequence in context: A214773 A076201 A129668 * A004687 A097895 A023182 Adjacent sequences:  A086788 A086789 A086790 * A086792 A086793 A086794 KEYWORD easy,nonn AUTHOR Cino Hilliard (hillcino368(AT)gmail.com), Aug 04 2003; corrected Jul 24 2004 STATUS approved

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Last modified May 26 02:53 EDT 2013. Contains 225653 sequences.