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A008559 a(1)=2; thereafter, convert a(n-1) from base 10 to base 2 but regard the result as a base 10 number.

%I A008559 #51 Feb 02 2025 12:10:23
%S A008559 2,10,1010,1111110010,1000010001110100011000101111010
%N A008559 a(1)=2; thereafter, convert a(n-1) from base 10 to base 2 but regard the result as a base 10 number.
%C A008559 The previous number is converted to binary digits and then the digits are regarded as decimal digits in the next number in the sequence. - _Michael Somos_, May 16 2014
%C A008559 The next term has 100 digits. - _Harvey P. Dale_, Jul 16 2011
%C A008559 The number of decimal digits of a(n) is A242347(n). - _Robert G. Wilson v_, Jul 10 2013
%C A008559 log(a(n))/log(a(n-1)) ~ log_2(10) = A020862. - _Robert G. Wilson v_, Jul 10 2013
%D A008559 Clifford Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
%H A008559 Vincenzo Librandi, <a href="/A008559/b008559.txt">Table of n, a(n) for n = 1..7</a>
%p A008559 f:=proc(n) local i,j,r; i:=convert(n,base,2); j:=add(i[r]*10^(r-1),r=1..nops(i)); end;
%p A008559 g:=proc(n,M) global f; local a,b,t1; a:=n; t1:=[a]; for i from 1 to M do b:=f(a); t1:=[op(t1),b]; a:=b; od; t1; end; g(2,5); # _N. J. A. Sloane_, Jul 14 2015
%t A008559 NestList[FromDigits[IntegerDigits[#,2]]&,2,5] (* _Harvey P. Dale_, Jul 16 2011 *)
%o A008559 (Python)
%o A008559 A008559_list = [2]
%o A008559 for _ in range(5):
%o A008559     A008559_list.append(int(bin(A008559_list[-1])[2:]))
%o A008559 # _Chai Wah Wu_, Dec 26 2014
%o A008559 (PARI) lista(nn) = my(k=2); print1(k); for(n=2, nn, print1(", ", k=fromdigits(binary(k)))); \\ _Jinyuan Wang_, Jan 18 2025
%Y A008559 Cf. A006937 (essentially the same sequence).
%Y A008559 For initial terms 2 through 12 see A008559, A006938, A260025, A260024, A260026, A260027, A260028, A260029, A008559 (again), A006938 (again), A260030 respectively.
%K A008559 nonn,base,nice
%O A008559 1,1
%A A008559 _N. J. A. Sloane_
%E A008559 Comment corrected by _Chai Wah Wu_, Dec 26 2014