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 A042972 #51 Sep 08 2022 08:44:55 %S A042972 4,8,1,0,4,7,7,3,8,0,9,6,5,3,5,1,6,5,5,4,7,3,0,3,5,6,6,6,7,0,3,8,3,3, %T A042972 1,2,6,3,9,0,1,7,0,8,7,4,6,6,4,5,3,4,9,4,0,0,2,0,8,1,5,4,8,9,2,4,2,5, %U A042972 5,1,9,0,4,8,9,1,5,8,2,1,3,6,7,4,8,7,0,4,7,6,6,5,8,3,8,8,3,3,5,4 %N A042972 Decimal expansion of i^(-i), where i = sqrt(-1). %C A042972 Square root of Gelfond's constant (A039661). Since Gelfond's constant e^Pi is transcendental, e^(Pi/2) is transcendental. - _Daniel Forgues_, Apr 15 2011 %C A042972 The complex sequence (...((((i)^i)^i)^i)^...) (n pairs of brackets) is periodic with period 4 and the first four entries are i, e^(-Pi/2), -i, e^(+Pi/2). See A049006 for e^(-Pi/2). - _Wolfdieter Lang_, Apr 27 2013 %C A042972 A solution of x^i + x^(-i) = 0. In fact, x = Exp(Pi/2 + k*Pi), where k is any integer. - _Robert G. Wilson v_, Feb 04 2014 %H A042972 Nathaniel Johnston, <a href="/A042972/b042972.txt">Table of n, a(n) for n = 1..10000</a> %H A042972 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 A042972 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A042972 Equals i^(-i) = i^(1/i) = e^(Pi/2). %F A042972 Also (((i)^i)^i)^i. See a comment above on such powers. - _Wolfdieter Lang_, Apr 27 2013 %e A042972 4.81047738096535165547303566670383312639017087466453494002... %p A042972 evalf[110](I^(-I)); # _Muniru A Asiru_, Feb 17 2019 %t A042972 RealDigits[Re[I^(1/I)], 10, 100][[1]] (* _Alonso del Arte_, Oct 31 2011 *) %t A042972 RealDigits[ Exp[Pi/2], 10, 111][[1]] (* _Robert G. Wilson v_, Apr 08 2014 *) %o A042972 (PARI) default(realprecision, 110); exp(Pi/2) \\ _Nathaniel Johnston_, Apr 15 2011 (modified by _G. C. Greubel_, Feb 17 2019) %o A042972 (Magma) SetDefaultRealField(RealField(110)); R:= RealField(); Exp(Pi(R)/2); // _G. C. Greubel_, Feb 17 2019 %o A042972 (Sage) numerical_approx(exp(pi/2), digits=110) # _G. C. Greubel_, Feb 17 2019 %Y A042972 Cf. A049006. %K A042972 cons,nonn %O A042972 1,1 %A A042972 _Marvin Ray Burns_ %E A042972 a(100) corrected by _Nathaniel Johnston_, Apr 15 2011