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A087165
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a(n)=1 when n==1 (mod 4), else a(n)=a(n-ceil(n/4))+1. Removing all the 1's results in the original sequence with every term incremented by 1.
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1
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1, 2, 3, 4, 1, 5, 2, 6, 1, 3, 7, 2, 1, 4, 8, 3, 1, 2, 5, 9, 1, 4, 2, 3, 1, 6, 10, 2, 1, 5, 3, 4, 1, 2, 7, 11, 1, 3, 2, 6, 1, 4, 5, 2, 1, 3, 8, 12, 1, 2, 4, 3, 1, 7, 2, 5, 1, 6, 3, 2, 1, 4, 9, 13, 1, 2, 3, 5, 1, 4, 2, 8, 1, 3, 6, 2, 1, 7, 4, 3, 1, 2, 5, 10, 1, 14, 2, 3, 1, 4, 6, 2, 1, 5, 3, 9, 1, 2, 4, 7, 1, 3, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Indices of records are given by A087192: a(A087192(n))=n, where A087192(n) = ceiling(A087192(n-1)*4/3).
To construct the sequence: Step 1: start from a sequence of 1 and leave 3 undefined places between two 1 giving: 1,(),(),(),1,(),(),(),1,(),(),(),1,(),(),(),1,(),(),(),1,... Step 2: replace the first undefined place with a 2 and leave 3 undefined places between two 2 giving: 1,2,(),(),1,(),2,(),1,(),(),2,1,(),(),(),1,2,(),(),1,... Step 3: replace the first undefined place with a 3 and leave 3 undefined places between two 3 giving: 1,2,3,(),1,(),2,(),1,3,(),2,1,(),(),3,1,2,(),(),1,... Step 4: replace the first undefined place with a 4 and leave 3 undefined places between two 4 giving: 1,2,3,4,1,(),2,(),1,3,(),2,1,4,(),3,1,2,(),(),1,... Iterating the process indefinitely yields the sequence: 1,2,3,4,1,5,2,6,1,3,7,2,1,4,8,3,1,2,5,9,1,... [From Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 07 2009]
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CROSSREFS
| Cf. A001511, A087088, A087192.
a(n+1)-a(n) = 4*A018902(n-3), n>2.
Sequence in context: A117742 A117716 A097150 * A083480 A179547 A023133
Adjacent sequences: A087162 A087163 A087164 * A087166 A087167 A087168
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 24 2003
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