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Search: id:A129751
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| A129751 |
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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. |
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+0
2
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| 0, 102, 101022, 101021010222, 101021010221010210102222, 101021010221010210102221010210102210102101022222, 10102101022101021010222101021010221010210102222101021010221010210102221010210102\ 2101021010222222
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Other sequences may be obtained by using different substitutions for '0', '{' and '}'.
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REFERENCES
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http://planetmath.org/encyclopedia/VonNeumannInteger.html
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LINKS
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I.N. Galidakis, Home Page
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FORMULA
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S(n)=n union {n}
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EXAMPLE
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a(0)=0, a(1)={0}=102, a(2)={0,{0}}=101022, etc.
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MAPLE
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N:=proc(n) local i, s, l, r, data; s:=`0`; l:=`1`; r:=`2`; #change here for different sequences 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:
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CROSSREFS
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Cf. A129754.
Adjacent sequences: A129748 A129749 A129750 this_sequence A129752 A129753 A129754
Sequence in context: A088805 A030512 A097725 this_sequence A094095 A074675 A161402
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KEYWORD
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easy,nonn
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AUTHOR
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I.N. Galidakis (jgal(AT)ath.forthnet.gr), May 14 2007
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