The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049006 Decimal expansion of i^i = exp(-Pi/2). 22
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Equals 1/A042972. - Lekraj Beedassy, Sep 02 2005 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 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 REFERENCES Florian Cajori, History of Mathematics. New York: Chelsea Publishing Company for the American Mathematical Society (1991): 236. Ian Connell, Modern Algebra: A Constructive Introduction. New York: Elsevier (1981) p. 363. Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 97. Reinhold Remmert, Theory of Complex Functions: Readings in Mathematics. New York: Springer-Verlag (1991): 162. LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Leonhard Euler, Letter to Christian Goldbach, Berlin, June 14 1746. Simon Plouffe, exp(-Pi/2) also i**i to 2000 digits Simon Plouffe, exp(-Pi/2) also i**i to 10000 digits H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116. Eric Weisstein's World of Mathematics, i. EXAMPLE 0.20787957635076190854695561983497877003387... MATHEMATICA RealDigits[Re[N[I^I, 100]]][[1]] PROG (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 (PARI) digits(exp(-Pi/2)\.1^default(realprecision))[^-1] \\ M. F. Hasler, May 17 2018 CROSSREFS Cf. A049007, A202501 (tetration). Cf. A077589 and A077590 for i^i^i^... Sequence in context: A243444 A256293 A272002 * A211113 A011389 A021485 Adjacent sequences:  A049003 A049004 A049005 * A049007 A049008 A049009 KEYWORD nonn,cons,changed AUTHOR Deepak R. N (deepak_rama(AT)bigfoot.com) STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 04:18 EDT 2021. Contains 345055 sequences. (Running on oeis4.)