This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049006 #63 Feb 16 2025 08:32:40
%S A049006 2,0,7,8,7,9,5,7,6,3,5,0,7,6,1,9,0,8,5,4,6,9,5,5,6,1,9,8,3,4,9,7,8,7,
%T A049006 7,0,0,3,3,8,7,7,8,4,1,6,3,1,7,6,9,6,0,8,0,7,5,1,3,5,8,8,3,0,5,5,4,1,
%U A049006 9,8,7,7,2,8,5,4,8,2,1,3,9,7,8,8,6,0,0,2,7,7,8,6,5,4,2,6,0,3,5
%N A049006 Decimal expansion of i^i = exp(-Pi/2).
%C A049006 Equals 1/A042972. - _Lekraj Beedassy_, Sep 02 2005
%C A049006 Euler knew this number to be purely real, and called the fact "remarkable" in a letter to Goldbach dated June 14, 1746. - _Alonso del Arte_, Nov 30 2012
%C A049006 The value follows immediately from Euler's formula i = exp(i Pi/2) and the rule (a^b)^c = a^(b*c). - The value given by Uhler has the final digits ...14 instead ...08, which is compatible with the claimed accuracy of 52 digits. - _M. F. Hasler_, May 17 2018
%D A049006 Florian Cajori, History of Mathematics. New York: Chelsea Publishing Company for the American Mathematical Society (1991): 236.
%D A049006 Ian Connell, Modern Algebra: A Constructive Introduction. New York: Elsevier (1981) p. 363.
%D A049006 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.11, p. 449.
%D A049006 Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 97.
%D A049006 Reinhold Remmert, Theory of Complex Functions: Readings in Mathematics. New York: Springer-Verlag (1991): 162.
%D A049006 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 26.
%H A049006 Harry J. Smith, <a href="/A049006/b049006.txt">Table of n, a(n) for n = 0..20000</a>
%H A049006 Leonhard Euler, <a href="https://math.dartmouth.edu/~euler/correspondence/letters/OO0820.pdf">Letter to Christian Goldbach</a>, Berlin, June 14 1746.
%H A049006 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/exppi2.txt">exp(-Pi/2) also i**i to 10000 digits</a>.
%H A049006 H. S. Uhler, <a href="http://www.jstor.org/stable/2972387">On the numerical value of i^i</a>, Amer. Math. Monthly, 28 (1921), 114-116.
%H A049006 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/i.html">i</a>.
%H A049006 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A049006 Equals 1/A042972 = 2*A097665. - _Hugo Pfoertner_, Aug 21 2024
%e A049006 0.20787957635076190854695561983497877003387...
%t A049006 RealDigits[Re[N[I^I, 100]]][[1]]
%o A049006 (PARI) { default(realprecision, 20080); x=10*exp(-Pi/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b049006.txt", n, " ", d)); } \\ _Harry J. Smith_, Apr 28 2009, corrected May 19 2009
%o A049006 (PARI) digits(exp(-Pi/2)\.1^default(realprecision))[^-1] \\ _M. F. Hasler_, May 17 2018
%Y A049006 Cf. A042972, A049007, A097665, A202501 (tetration).
%Y A049006 Cf. A077589 and A077590 for i^i^i^...
%K A049006 nonn,cons
%O A049006 0,1
%A A049006 Deepak R. N (deepak_rama(AT)bigfoot.com)