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 A039661 Decimal expansion of exp(Pi). 36
 2, 3, 1, 4, 0, 6, 9, 2, 6, 3, 2, 7, 7, 9, 2, 6, 9, 0, 0, 5, 7, 2, 9, 0, 8, 6, 3, 6, 7, 9, 4, 8, 5, 4, 7, 3, 8, 0, 2, 6, 6, 1, 0, 6, 2, 4, 2, 6, 0, 0, 2, 1, 1, 9, 9, 3, 4, 4, 5, 0, 4, 6, 4, 0, 9, 5, 2, 4, 3, 4, 2, 3, 5, 0, 6, 9, 0, 4, 5, 2, 7, 8, 3, 5, 1, 6, 9, 7, 1, 9, 9, 7, 0, 6, 7, 5, 4, 9, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS e^Pi and Pi^e (A059850) differ by hardly 3% in magnitude. The determination of the inequality sign between them does not require their actual evaluation, the result being immediate from the basic facts Pi>e and log(x+1)0) yields log(Pi)=0} (u(j+1)/u(j))^2^(-j+1)) where u(0)=1 and v(0)=1/sqrt(2); u(n+1) = u(n)/2 + v(n)/2, v(n+1) = sqrt(u(n)v(n)) (deduced from Salamin algorithm for Pi). - Benoit Cloitre, Aug 14 2003 e^Pi = Sum_{k>=0} a(k)/k!/2^k where a(0)=1, a(1)=6 and a(n) = (40 - 4*n + n^2)*a(n-2) for n>=2 (from expansion of exp(6*asin(x)) at x=1/2). - Jaume Oliver Lafont, Oct 21 2009 exp(Pi) ~= log(Pi) + 7*Pi. - Alexander R. Povolotsky, Oct 24 2009 Equals Sum_{k>=0} Pi^k/k!. - Paolo Xausa, Nov 14 2021 EXAMPLE 23.1406926327792690... MATHEMATICA RealDigits[N[E^Pi, 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *) PROG (PARI) default(realprecision, 20080); x=exp(1)^Pi/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b039661.txt", n, " ", d)); \\ Harry J. Smith, Apr 18 2009 (PARI) A039661(n)=default(realprecision, n); exp(Pi)\10^(3-n)%10 \\ M. F. Hasler, Oct 24 2009 CROSSREFS Cf. A059850 (Pi^e). Cf. A058287 = contfrac(e^Pi), A058288 = contfrac(Pi^e). Sequence in context: A306646 A152832 A211343 * A293668 A214684 A268727 Adjacent sequences:  A039658 A039659 A039660 * A039662 A039663 A039664 KEYWORD nonn,cons AUTHOR STATUS approved

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Last modified September 30 21:21 EDT 2022. Contains 357106 sequences. (Running on oeis4.)