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Search: id:A155890
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| A155890 |
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a(n+1) is the least integer > a(n) containing all digits of a(n); a(1)=2. |
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+0
1
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| 2, 12, 21, 102, 120, 201, 210, 1002, 1020, 1200, 2001, 2010, 2100, 10002, 10020, 10200, 12000, 20001, 20010, 20100, 21000, 100002, 100020, 100200, 102000, 120000, 200001, 200010, 200100, 201000, 210000, 1000002, 1000020, 1000200, 1002000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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We can easily show that : (1) All terms have digits less than 3. (2) For m>1, a m-digit term of S has m-2 zero's, one 1 and one 2. (3) For m>1, the set A(m) of m-digit terms of S has 2m-2 members and A(m)=Join[Table[10^(m-1)+2*10^t,{t,0,m-2}],Table[2*10^(m-1)+10^t,{t,0,m-2}]] (4) For each m, at index n=m^2-m+2 number of digits of a(n) equals to 1+number of digits of a(n-1). - F. Firoozbakht
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MATHEMATICA
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/* Mmca code for generating all terms less than 10^m, m>1 (the first m^2-m+1 terms) - by F. Firoozbakht */ n=m; A[n_]:=Join[Table[10^(n-1)+2*10^t, {t, 0, n-2}], Table[2*10^(n-1)+10^t, {t, 0, n-2}]]; v={2}; Do[v=Join[v, A[k]], {k, 2, n}]; v
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CROSSREFS
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Adjacent sequences: A155887 A155888 A155889 this_sequence A155891 A155892 A155893
Sequence in context: A058413 A053890 A053896 this_sequence A077410 A063599 A163479
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KEYWORD
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base,nonn
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AUTHOR
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E. Angelini (Eric.Angelini(AT)kntv.be), F. Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir) and M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 01 2009
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