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A106448
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Table of (x+y)/gcd(x,y) where (x,y) runs through the pairs (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
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3
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2, 3, 3, 4, 2, 4, 5, 5, 5, 5, 6, 3, 2, 3, 6, 7, 7, 7, 7, 7, 7, 8, 4, 8, 2, 8, 4, 8, 9, 9, 3, 9, 9, 3, 9, 9, 10, 5, 10, 5, 2, 5, 10, 5, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 7, 14, 7, 14, 7, 2, 7, 14, 7, 14, 7, 14
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OFFSET
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1,1
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COMMENTS
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Can also be viewed as a triangular table T(n,k) (n>=1, 1<=k<=n) read by rows: T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3); T(4,1), T(4,2), T(4,3), T(4,4); ... where T(n,k) gives the least value v>0 such that v*k = 0 modulo n+1, i.e., in other words, T(n,k) = (n+1)/gcd(n+1,k).
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LINKS
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FORMULA
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T(n, k) = numerator((n+k)/n) = numerator((n+k)/k). - Michel Marcus, Dec 29 2013
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EXAMPLE
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The top left corner of the square array is:
2 3 4 5 6 7 8 9 10 11 ...
3 2 5 3 7 4 9 5 11 ...
4 5 2 7 8 3 10 11 ...
5 3 7 2 9 5 11 ...
6 7 8 9 2 11 ...
7 4 3 5 11 ...
8 9 10 11 ...
9 5 11 ...
10 11 ...
11 ...
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CROSSREFS
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GF(2)[X] analog: A106449. Row 1 is n+1, row 2 is LEFT(LEFT(LEFT(A026741))), row 3 is LEFT^4(A051176). Essentially the same as A054531, but without its right-hand edge of all-1's.
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KEYWORD
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AUTHOR
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STATUS
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approved
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