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 A327603 #31 Jan 11 2020 15:57:47
%S A327603 1,1,3,39,617,10922,217833,4871823,121210687,3327237897,100000000001,
%T A327603 3268336354411,115465060699617,4386014250379643,178300955775879752,
%U A327603 7725047653062230514,355393490465494856466,17303907095298306637188,889028356166899850147118
%N A327603 Number of digits in (n^n)^(n^n).
%C A327603 a(0) = 1 whether we take 0^0 = 1 or 0^0 = 0.
%C A327603 The standard simplification of (n^n)^(n^n) is n^(n^(n+1)). - _M. F. Hasler_, Oct 15 2019
%F A327603 a(n) = 1 + floor(n^(n+1) * log_10(n)).
%F A327603 a(10^k) = k * 10^(k*(10^k + 1)) + 1. - _Jon E. Schoenfield_, Sep 29 2019
%F A327603 a(n) = A055642(A004217(n)), n > 0. - _Felix Fröhlich_, Oct 15 2019
%e A327603 a(10) = 1 + floor(10^(10+1) * log_10(10)) = 1 + floor( 100000000000 * 1) = 100000000001.
%e A327603 a(10^3) = 3*10^3003 + 1.
%t A327603 Table[IntegerLength[(n^n)^(n^n)], {n, 1, 8}] (* Human friendly *)
%t A327603 Table[1 + Floor[n^(n + 1) * Log10[n]], {n, 1, 16}] (* Computationally efficient *)
%o A327603 (PARI) a(n) = my(x=n^n); 1 + floor(x*log(x)/log(10));
%o A327603 (PARI) A327603(n,L=log(10))=n^(n+1)*log(n)\L+1 \\ Supplying the 2nd arg allows to avoid re-computation of log(10) on each call, and also to get the number of digits in any desired base. - _M. F. Hasler_, Oct 15 2019
%Y A327603 Cf. A004217, A054382, A055642, A066022.
%K A327603 nonn,base
%O A327603 0,3
%A A327603 _Natan Arie Consigli_, Sep 22 2019
%E A327603 a(9)-a(15) from _Nathaniel Johnston_, Sep 23 2019
%E A327603 a(13)-a(15) corrected and a(16) appended by _Natan Arie Consigli_, Sep 25 2019
%E A327603 a(17)-a(18) from _Jon E. Schoenfield_, Sep 29 2019