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A094008
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Primes which are the denominators of convergents of the continued fraction expansion of e.
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6
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OFFSET
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1,1
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COMMENTS
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LINKS
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J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010; arXiv:0709.0671 [math.NT], 2007-2009.
Eric Weisstein's World of Mathematics, e.
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FORMULA
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EXAMPLE
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a(1) = 3 because 3 is the first prime denominator of a convergent, 8/3, of the simple continued fraction for e
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MATHEMATICA
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Block[{$MaxExtraPrecision=1000}, Select[Denominator[Convergents[E, 500]], PrimeQ]] (* Harvey P. Dale, Aug 23 2011 *)
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PROG
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(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
); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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