A367033 - OEIS

%I #111 Dec 12 2024 23:12:02

%S 1,3,39,9807,642665631,2760227864398567743,

%T 50917216999682251351660181504218706559,

%U 17326231117678921325668214077168498563134593883851671914433735718213795341567

%N Von Neumann ordinals in bracket notation encoded by binary bits: '{' -> 0, '}'-> 1.

%C If brackets are interpreted as 90-degree turns, and left bracket is turn left and go forward 1 unit, right bracket is turn right and go forward 1 unit, then a Levy C curve is drawn.

%e For n=3, Von Neumann's 3-element set {0, 1, 2} is

%e    { {}, {{}}, {{},{{}}} }

%e    0 01  0011  001 00111 1 binary = a(3) = 9807

%t With[{nmax=8},Map[FromDigits[#,2]&,NestList["0"<>StringTake[#,{2,-2}]<>#<>"1"&,"01",nmax]]] (* _Paolo Xausa_, Nov 20 2023 *)

%o (PARI) a(n) = my(k = 1); for(m = 1, n, k = (k-1)*2^(2^m)+2*k+1); k; \\ _Thomas Scheuerle_, Nov 21 2023

%o (Python)

%o from functools import lru_cache

%o @lru_cache(maxsize=None)

%o def A367033(n): return 1-(m:=1<<(2<<n-1)) +(m+2)*A367033(n-1) if n>0 else 1

%Y Cf. A092124 (bit complement), A333447 (bit reversal), A308187 (individual bits).

%K nonn,base,easy

%O 0,2

%A _Stuart E Anderson_, Nov 20 2023

%E a(7) from _Paolo Xausa_, Nov 20 2023

%E Offset corrected by _Kevin Ryde_, Dec 24 2023