A092124 a(0) = 2, a(n) = (2^(2^n)+2)*a(n-1) for n>0.

2, 12, 216, 55728, 3652301664, 15686516209310983872, 289365149921256212111714425927549504896, 98465858119637274097902770931519409290135390781788892125023848289699334298368

Offset: 0

Author

Reinhard Zumkeller, Mar 30 2004

Keywords

• nonn

Comments

In binary representation a(n) can be interpreted as an expression to represent n according to John von Neumann's definition of natural numbers: braces are coded as 1 and 0 and the empty set as 10={};

a(n) = (A001146(n)+2)*a(n-1) = 2*(A058891(n)+1)*a(n-1).

Examples

			a(3)=55728='1101100110110000' -> {{}{{}}{{}{{}}}} -> {{},{{}},{{},{{}}}} -> {0,{0},{0,{0}}} -> {0,1,{0,1}} -> {0,1,2} -> A001477(3)=3.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A001146, A058891, A333447, A367033.

Programs

Mathematica

RecurrenceTable[{a[0]==2,a[n]==(2^(2^n)+2)a[n-1]},a,{n,8}] (* Harvey P. Dale, Nov 15 2020 *)
nxt[{n_,a_}]:={n+1,(2^2^(n+1)+2)a}; NestList[nxt,{0,2},8][[;;,2]] (* Harvey P. Dale, Aug 11 2023 *)

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A092124(n): return ((1<<(1<A092124(n-1) if n else 2 # Chai Wah Wu, Nov 23 2023