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 A242347 #42 May 22 2025 10:21:38
%S A242347 1,2,4,10,31,100,330,1093,3628,12049,40023,132951,441651,1467130,
%T A242347 4873698,16190071,53782249,178660761,593498199,1971558339
%N A242347 Number of decimal digits of A008559.
%C A242347 a(n+1)/a(n) is approximately log_2(10) = A020862. - _André Engels_, Apr 01 2021
%H A242347 Code Golf StackExchange, <a href="https://codegolf.stackexchange.com/questions/253857/length-of-binary-as-base-10-oeis-a242347">Length of Binary as Base 10 [OEIS A242347]</a>, coding challenge started Oct 28 2022.
%F A242347 a(n) = A055642(A008559(n)). - _Michel Marcus_, May 11 2014
%e A242347 a(3) = 4 because 1010 has 4 decimal digits.
%o A242347 (Python)
%o A242347 A242347_list, l = [1], 2
%o A242347 for _ in range(10):
%o A242347 l = int(bin(l)[2:])
%o A242347 A242347_list.append(len(str(l))) # _Chai Wah Wu_, Dec 26 2014
%o A242347 (PARI) a242347(n) = {my (k=2, d=digits); while(n--, k=fromdigits(d(k,2))); #d(k)} \\ _Hugo Pfoertner_, Nov 04 2022
%Y A242347 Cf. A008559, A055642, A020862.
%K A242347 nonn,base,more
%O A242347 1,2
%A A242347 _J. Lowell_, May 11 2014
%E A242347 a(1), a(18)-a(20) from _Chai Wah Wu_, Dec 26 2014