OFFSET
1,1
COMMENTS
The position of a(n) in A000040 (the prime numbers) is A102049(n) = A000720(a(n)). - Jonathan Sondow, Dec 27 2004
The next term has 166 digits. [Harvey P. Dale, Aug 23 2011]
LINKS
Joerg Arndt, Table of n, a(n) for n = 1..10
E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641 (article), 114 (2007) 659 (addendum).
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010.
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.
EXAMPLE
a(1) = 3 because 3 is the first prime denominator of a convergent, 8/3, of the simple continued fraction for e
MATHEMATICA
Block[{$MaxExtraPrecision=1000}, Select[Denominator[Convergents[E, 500]], PrimeQ]] (* Harvey P. Dale, Aug 23 2011 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Apr 20 2004
STATUS
approved