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A194258
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Second inverse function (numbers of columns) for pairing function A060734.
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2
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1, 1, 2, 2, 1, 2, 3, 3, 3, 1, 2, 3, 4, 4, 4, 4, 1, 2, 3, 4, 5, 5, 5, 5, 5, 1, 2, 3, 4, 5, 6, 6, 6, 6, 6, 6, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 1, 2, 3, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 2, 3, 4, 5, 6
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OFFSET
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1,3
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COMMENTS
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The sequence is the first inverse function (numbers of rows) for pairing function A060736.
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LINKS
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FORMULA
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a(n) = min{t; n - (t - 1)^2}, where t=floor(sqrt(n-1))+1.
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EXAMPLE
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The start of the sequence as triangle array read by rows:
1;
1,2,2;
1,2,3,3,3;
1,2,3,4,4,4,4;
. . .
Row number k contains 2k-1 numbers 1,2,...k-1,k,k,...k (k times repetition "k").
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MATHEMATICA
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Flatten[Table[Join[Range[n-1], Table[n, {n}]], {n, 10}]] (* Harvey P. Dale, Jun 23 2013 *)
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PROG
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(Python)
t=int(math.sqrt(n-1)) +1
j=min(t, n-(t-1)**2)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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