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A243070
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Square array read by antidiagonals: rows are successively recursivized versions of Bulgarian solitaire operation (starting from the usual "first order" version, A242424), as applied to the partitions listed in A112798.
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10
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1, 2, 1, 4, 2, 1, 3, 4, 2, 1, 6, 3, 4, 2, 1, 6, 8, 3, 4, 2, 1, 10, 6, 8, 3, 4, 2, 1, 5, 12, 6, 8, 3, 4, 2, 1, 12, 5, 16, 6, 8, 3, 4, 2, 1, 9, 9, 5, 16, 6, 8, 3, 4, 2, 1, 14, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 10, 20, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 22, 10, 24, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 15, 28, 10, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 18, 18, 40, 10, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1
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OFFSET
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1,2
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COMMENTS
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The array is read by antidiagonals: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... .
Please see comments and references in A242424 for more information about Bulgarian Solitaire.
Rows in both arrays converge towards A122111.
All the terms in column n are multiples of A105560(n).
The rows of this table (i.e., the corresponding functions) preserve A056239.
First point where row k differs from row k of A243060 seems to be A000040(k+2): primes from five onward: 5, 7, 11, 13, 17, 19, 23, 29, 31, ... and these seem to be also the points where that row differs for the first time from A122111.
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LINKS
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FORMULA
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EXAMPLE
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The top left corner of the array is:
1, 2, 4, 3, 6, 6, 10, 5, 12, 9, 14, 10, 22, 15, 18, ...
1, 2, 4, 3, 8, 6, 12, 5, 9, 12, 20, 10, 28, 18, 18, ...
1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 24, 10, 40, 24, 18, ...
1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 48, 24, 18, ...
1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 64, 24, 18, ...
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PROG
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(Scheme)
(define (A243070bi row col) (cond ((<= col 1) col) ((= 1 row) (A242424 col)) (else (* (A000040 (A001222 col)) (A243070bi (- row 1) (A064989 col))))))
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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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