A129751 The natural numbers represented by their set theoretic Von Neumann construction, where the empty set is replaced by '0', the left set bracket '{' is replaced by 1, the right bracket '}' is replaced by 2 and the set construct contents are ordered by increasing cardinality.

0, 102, 101022, 101021010222, 101021010221010210102222, 101021010221010210102221010210102210102101022222, 101021010221010210102221010210102210102101022221010210102210102101022210102101022101021010222222

Offset

0,2

Links

Table of n, a(n) for n=0..6.

PlanetMath, von Neumann integer

Example

a(0)=0, a(1)={0}=102, a(2)={0,{0}}=101022, etc.

Maple

N:=proc(n) local i, s, l, r, data; s:=`0`; l:=`1`; r:=`2`; if n>0 then for i from 1 to n-1 do s:=cat(s, l, s, r); od; s:=cat(l, s, r); fi; data:=sscanf(s, `%d`); RETURN(data[1]); end:

Mathematica

Join[{0}, Map[FromDigits, NestList["1"<>StringTake[#, {2, -2}]<>#<>"2"&, "102", 7]]] (* Paolo Xausa, Nov 22 2023 *)

Crossrefs

Cf. A129754.

Sequence in context: A030512 A097725 A353142 * A225993 A237432 A370404

Adjacent sequences: A129748 A129749 A129750 * A129752 A129753 A129754

Keyword

easy,nonn,base

Author

I.N. Galidakis (jgal(AT)ath.forthnet.gr), May 14 2007

Status

approved