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A230417
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Lower triangular region of A230415, a triangular table read by rows: T(n, k) tells in how many digit positions the factorial base representations (A007623) of n and k differ, where (n, k) = (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), ..., n >= 0 and (0 <= k <= n).
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5
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0, 1, 0, 1, 2, 0, 2, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 2, 2, 3, 2, 3, 0, 2, 1, 3, 2, 3, 2, 1, 0, 2, 3, 1, 2, 2, 3, 1, 2, 0, 3, 2, 2, 1, 3, 2, 2, 1, 1, 0, 2, 3, 2, 3, 1, 2, 1, 2, 1, 2, 0, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 0, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 0, 2, 1, 3, 2, 3, 2, 2, 1, 3, 2, 3, 2, 1, 0, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 1, 2, 0
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = A230415bi(A003056(n),A002262(n)). [As a sequence, this is obtained by taking a subsection from array A230415.]
T(n,0) = A060130(n) [the leftmost column].
For n >= 1, T(n,n-1) = A055881(n) [the last nonzero column].
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EXAMPLE
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This triangular table begins:
0;
1, 0;
1, 2, 0;
2, 1, 1, 0;
1, 2, 1, 2, 0;
2, 1, 2, 1, 1, 0;
1, 2, 2, 3, 2, 3, 0;
...
Please see A230415 for examples showing how the terms are computed.
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PROG
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(Scheme)
(define (A230415bi x y) (let loop ((x x) (y y) (i 2) (d 0)) (cond ((and (zero? x) (zero? y)) d) (else (loop (floor->exact (/ x i)) (floor->exact (/ y i)) (+ i 1) (+ d (if (= (modulo x i) (modulo y i)) 0 1)))))))
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CROSSREFS
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This is a lower, or equivalently, an upper triangular subregion of symmetric square array A230415.
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KEYWORD
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AUTHOR
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STATUS
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approved
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