cp's OEIS Frontend

A086791 Primes found among the numerators of the continued fraction rational approximations to e.

%I A086791 #28 Nov 18 2019 01:37:44
%S A086791 2,3,11,19,193,49171,1084483,563501581931,332993721039856822081,
%T A086791 3883282200001578119609988529770479452142437123001916048102414513139044082579
%N A086791 Primes found among the numerators of the continued fraction rational approximations to e.
%H A086791 Joerg Arndt, <a href="/A086791/b086791.txt">Table of n, a(n) for n = 1..11</a>
%H A086791 Cino Hilliard, <a href="http://web.archive.org/web/20080411094846/http://groups.msn.com/BC2LCC/continuedfractions.msnw">Continued fractions rational approximation of numeric constants</a>.
%e A086791 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.
%o A086791 (PARI)
%o A086791 \\ Continued fraction rational approximation of numeric constants f. m=steps.
%o A086791 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,",")); ) }
%o A086791 (PARI)
%o A086791 default(realprecision,10^5);
%o A086791 cf=contfrac(exp(1));
%o A086791 n=0;
%o A086791 { for(k=1, #cf,  \\ generate b-file
%o A086791     pq = contfracpnqn( vector(k,j, cf[j]) );
%o A086791     p = pq[1,1];  q = pq[2,1];
%o A086791     if ( ispseudoprime(p), n+=1; print(n," ",p) );  \\ A086791
%o A086791 \\    if ( ispseudoprime(q), n+=1; print(n," ",q) );  \\ A094008
%o A086791 ); }
%o A086791 /* _Joerg Arndt_, Apr 21 2013 */
%Y A086791 Cf. A002119, A086788, A094008.
%K A086791 easy,nonn
%O A086791 1,1
%A A086791 _Cino Hilliard_, Aug 04 2003; corrected Jul 24 2004