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%I #14 Nov 22 2023 08:16:15
%S 0,102,101022,101021010222,101021010221010210102222,
%T 101021010221010210102221010210102210102101022222,
%U 101021010221010210102221010210102210102101022221010210102210102101022210102101022101021010222222
%N 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.
%H PlanetMath, <a href="http://planetmath.org/vonneumanninteger">von Neumann integer</a>
%e a(0)=0, a(1)={0}=102, a(2)={0,{0}}=101022, etc.
%p 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:
%t Join[{0},Map[FromDigits,NestList["1"<>StringTake[#,{2,-2}]<>#<>"2"&,"102",7]]] (* _Paolo Xausa_, Nov 22 2023 *)
%Y Cf. A129754.
%K easy,nonn,base
%O 0,2
%A I.N. Galidakis (jgal(AT)ath.forthnet.gr), May 14 2007
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