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 A006938 M4814 #43 Jan 18 2025 16:35:34
%S A006938 3,11,1011,1111110011,1000010001110100011000101111011
%N A006938 Convert the last term from decimal to binary! a(1)=3.
%C A006938 The next term (a(6)) has 100 digits. - _Harvey P. Dale_, Feb 28 2012
%C A006938 The number of digits of a(n) are 1, 2, 4, 10, 31, 100, 330, 1093, 3628, 12049, 40023, 132951, 441651, 1467130, 4873698, 16190071, 53782249, 178660761, ... - _Robert G. Wilson v_, Jul 10 2013
%C A006938 log(a(n))/log(a(n-1)) ~ log_2(10) = A020862. - _Robert G. Wilson v_, Jul 10 2013
%D A006938 C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
%D A006938 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%t A006938 NestList[FromDigits[IntegerDigits[#,2]]&,3,4] (* _Harvey P. Dale_, Feb 28 2012 *)
%o A006938 (Python)
%o A006938 def agen(an):
%o A006938 while True: yield an; an = int(bin(an)[2:])
%o A006938 g = agen(3)
%o A006938 print([next(g) for i in range(5)]) # _Michael S. Branicky_, Mar 11 2021
%o A006938 (PARI) lista(nn) = my(k=3); print1(k); for(n=2, nn, print1(", ", k=fromdigits(binary(k)))); \\ _Jinyuan Wang_, Jan 18 2025
%Y A006938 For initial terms 2 through 12 see A008559, A006938, A260025, A260024, A260026, A260027, A260028, A260029, A008559 (again), A006938 (again), A260030 respectively.
%K A006938 nonn,base
%O A006938 1,1
%A A006938 _N. J. A. Sloane_
%E A006938 a(1)=3 added by _N. J. A. Sloane_, Jul 14 2015