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A278482
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Square array A(n,k): A(0, n) = n; A(k, n) = A(k-1, floor(n*(k+1)/k)), for k >= 1, read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
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4
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0, 1, 0, 2, 2, 0, 3, 4, 2, 0, 4, 6, 6, 2, 0, 5, 8, 8, 6, 2, 0, 6, 10, 12, 12, 6, 2, 0, 7, 12, 14, 14, 12, 6, 2, 0, 8, 14, 18, 18, 18, 12, 6, 2, 0, 9, 16, 20, 24, 24, 18, 12, 6, 2, 0, 10, 18, 24, 26, 26, 26, 18, 12, 6, 2, 0, 11, 20, 26, 30, 30, 30, 26, 18, 12, 6, 2, 0, 12, 22, 30, 36, 38, 38, 38, 26, 18, 12, 6, 2, 0
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OFFSET
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0,4
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COMMENTS
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Related to Flavius Josephus's sieve. See A278492 and the postings by David W. Wilson et al. on SeqFan list, Nov 22 2016.
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LINKS
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FORMULA
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A(0, n) = n for n >= 0; A(k, n) = A(k - 1, [n*(k + 1)/k]) for k > 0 and n >= 0. Here [ ] stands for floor-function. From David W. Wilson's posting to SeqFan list on 22 Nov 2016.
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EXAMPLE
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The top left corner of the array:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
0, 2, 4, 6, 8, 10, 12, 14, 16, 18
0, 2, 6, 8, 12, 14, 18, 20, 24, 26
0, 2, 6, 12, 14, 18, 24, 26, 30, 36
0, 2, 6, 12, 18, 24, 26, 30, 38, 42
0, 2, 6, 12, 18, 26, 30, 38, 42, 48
0, 2, 6, 12, 18, 26, 38, 42, 48, 60
0, 2, 6, 12, 18, 26, 38, 48, 60, 62
0, 2, 6, 12, 18, 26, 38, 48, 62, 66
0, 2, 6, 12, 18, 26, 38, 48, 62, 78
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MATHEMATICA
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t[k_, n_] := t[k - 1, Floor[n*(k + 1)/k]]; t[0, n_] = n; Table[t[k - 1, n - k + 1], {n, 0, 12}, {k, 1, n + 1}] // Flatten (* Robert G. Wilson v, Nov 23 2016 *)
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PROG
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(Scheme)
(define (A278482bi row col) (if (zero? row) col (A278482bi (- row 1) (floor->exact (* col (/ 1 row) (+ 1 row))))))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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