A367033 Von Neumann ordinals in bracket notation encoded by binary bits: '{' -> 0, '}'-> 1.

1, 3, 39, 9807, 642665631, 2760227864398567743, 50917216999682251351660181504218706559, 17326231117678921325668214077168498563134593883851671914433735718213795341567

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..7.

Example

For n=3, Von Neumann's 3-element set {0, 1, 2} is
   { {}, {{}}, {{},{{}}} }
   0 01  0011  001 00111 1 binary = a(3) = 9807

Mathematica

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

Prog

(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
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A367033(n): return 1-(m:=1<<(2<<n-1)) +(m+2)*A367033(n-1) if n>0 else 1

Crossrefs

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

Sequence in context: A188388 A076628 A198411 * A097421 A180418 A166999

Adjacent sequences: A367030 A367031 A367032 * A367034 A367035 A367036

Keyword

nonn,base,easy,changed

Author

Stuart E Anderson, Nov 20 2023

Extensions

a(7) from Paolo Xausa, Nov 20 2023

Offset corrected by Kevin Ryde, Dec 24 2023

Status

approved