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 A077589 #30 Feb 16 2025 08:32:48 %S A077589 4,3,8,2,8,2,9,3,6,7,2,7,0,3,2,1,1,1,6,2,6,9,7,5,1,6,3,5,5,1,2,6,4,8, %T A077589 2,4,2,6,7,8,9,7,3,5,1,6,4,6,3,9,4,6,0,3,6,0,9,2,2,1,2,4,0,4,9,5,7,9, %U A077589 1,5,3,2,2,2,2,6,9,5,6,8,7,6,6,9,1,7,2,1,4,0,5,3,8,2,0,4,0,7,5,4,9 %N A077589 Decimal expansion of real part of the infinite power tower of i. %C A077589 This is the real part of i^i^i^i^i^i... %D A077589 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.11, p. 449. %H A077589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/i.html">i</a>. %H A077589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>. %F A077589 The value is 2 (i/Pi) W(-i Pi/2) = 0.4382829... + i 0.360592..., where W denotes the principal branch of the Lambert W function. - David W. Cantrell, Nov 23 2007 %e A077589 0.43828293672703211162697516355126482426789735164639460360922124049579153222269568... %p A077589 evalf(Re(2*I*LambertW(-I*Pi/2)/Pi), 137); # _Alois P. Heinz_, Dec 12 2023 %t A077589 Prepend@@RealDigits[Re[ -ProductLog[ -Log[I]]/Log[I]], 10, 150] %o A077589 (PARI) z=(1+I)/2;e=.1^default(realprecision);until(e>abs(z-z-=(z-I^z)/(1-I^(z+1)*Pi/2)),);digits(real(z)\e) \\ _M. F. Hasler_, May 17 2018 %Y A077589 Cf. A049006, A077590 (imaginary part). %K A077589 nonn,cons,nice %O A077589 0,1 %A A077589 _Eric W. Weisstein_, Nov 07 2002