A129754 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, the set construct contents are ordered by increasing cardinality and the final number is interpreted in base 3.

0, 11, 278, 202040, 107371882880, 30324991112647875920960, 2418916677393691552133618294938847890243982720, 15390805926573768302084260548391044837412074858741153833336080616936611834819590898337488640

Offset

0,2

Links

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

Formula

S(n) = n union {n}.

Example

a(0)=0=0_3=0, a(1)={0}=102_3=11, a(2)={0,{0}}=101022_3=278, 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: b3tob10:=proc(n) local i, nl, sl, suma; if n=0 then suma:=0; else sl:=convert(n, base, 10); nl:=convert(sl, base, 3, 10); suma:=sum(nl[i]*10^(i-1), i=1..nops(nl)); fi; RETURN(suma); end: for n from 0 to 7 do b3tob10(N(n)); od;

Mathematica

Join[{0}, Map[FromDigits[#, 3]&, NestList["1"<>StringTake[#, {2, -2}]<>#<>"2"&, "102", 8]]] (* Paolo Xausa, Nov 22 2023 *)

Crossrefs

Cf. A129751.

Sequence in context: A062210 A049080 A210807 * A103547 A171195 A274780

Adjacent sequences: A129751 A129752 A129753 * A129755 A129756 A129757

Keyword

easy,nonn,base

Author

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

Extensions

Missing a(0) inserted by Paolo Xausa, Nov 22 2023

Status

approved