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A157261
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A run-length encoding of blocks of 2 in A090822.
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2
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1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3
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OFFSET
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1,4
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COMMENTS
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The assumption underlying this sequence is that the number 2 occurs isolated or in blocks of length 3 in A090822.
This sequence notes the size of successive blocks of length 3, that is, the number of blocks of length 3 not interrupted by an isolated 2.
This is equivalent to counting the successive triples of indices of the form k, k+1, k+2 in A157041.
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LINKS
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EXAMPLE
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A090822(n)=2 at n=3 (isolated), n=6-7 (block), n=12 (isolated), n=15-17 (block), n=19 (isolated), n=22 (isolated), n=25-27 (block), n=31 (isolated) n=34-36 (block), n=38-40 (block), n=42-44 (block), n=47 (isolated).
Determining the cluster size of successive blocks, we write a(1)=1 (block at n>=6), a(2)=1 (block at n>=15), a(3)=1 (block at n=>25), a(4)=3 (blocks at n>=34, n>=38, n>=42)), a(5)=1 (block at n>=53).
a(16)=9 represents the 9 blocks at n>=179, n>=183, n>=187, n>=192, n>=196, n>=200,... n>=213, followed by an isolated 2 at n=223.
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MATHEMATICA
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nmax = 2000;
A090822 = Cases[Import["https://oeis.org/A090822/b090822.txt", "Table"], {_, _}][[1 ;; nmax, 2]];
Length /@ DeleteCases[Split[DeleteCases[Split[A090822], s_List /; s[[1]] != 2] , #1 == #2 == {2, 2, 2}&], {{2}}] (* Jean-François Alcover, Sep 02 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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