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%I #15 Jun 08 2017 16:33:47
%S 0,0,0,0,1,2,0,1,0,2,0,1,2,1,4,0,1,2,3,0,4,0,1,2,3,4,1,6,0,1,2,3,4,5,
%T 6,6,0,1,2,3,4,5,0,7,8,0,1,2,3,4,5,6,1,6,8,0,1,2,3,4,5,6,7,2,7,10,0,1,
%U 2,3,4,5,6,7,8,3,6,10,0,1,2,3,4,5,6,7,8,9,4,7,12,0,1,2,3,4,5,6,7,8,9,10,5,12,12,0,1,2,3,4,5,6,7,8,9,10,11,0,13,14
%N Square array A(n,d): overwrite with zero the digit at position d from right (indicating radix d+2) in the factorial base representation of n, then convert back to decimal, read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc.
%H Antti Karttunen, <a href="/A275730/b275730.txt">Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F Other identities:
%F For all n >= 1, A(n,A084558(n)-1) = A257687(n).
%F For all n >= 0, A(n,A084558(n)) = n.
%e Columns 0-4 of rows 0 - 24 of the array:
%e 0, 0, 0, 0, 0, ... [No matter which digit of zero we clear, it stays zero forever]
%e 0, 1, 1, 1, 1 ... [When clearing the least significant digit (pos. 0) of one, "1", we get zero, and clearing any other digit past the most significant digit keeps one as one]
%e 2, 0, 2, 2, 2, ... [Clearing the least significant digit of 2, "10", doesn't affect it, but clearing the digit-1 zeros the whole number].
%e 2, 1, 3, 3, 3, ... [Clearing the least significant factorial base digit of 3 ("11") gives "10", 2, clearing the digit-1 gives "01" = 1, and clearing any digit past the most significant keeps "11" as it is, 3].
%e 4, 0, 4, 4, 4
%e 4, 1, 5, 5, 5
%e 6, 6, 0, 6, 6
%e 6, 7, 1, 7, 7
%e 8, 6, 2, 8, 8
%e 8, 7, 3, 9, 9
%e 10, 6, 4, 10, 10
%e 10, 7, 5, 11, 11
%e 12, 12, 0, 12, 12
%e 12, 13, 1, 13, 13
%e 14, 12, 2, 14, 14
%e 14, 13, 3, 15, 15
%e 16, 12, 4, 16, 16
%e 16, 13, 5, 17, 17
%e 18, 18, 0, 18, 18
%e 18, 19, 1, 19, 19
%e 20, 18, 2, 20, 20
%e 20, 19, 3, 21, 21
%e 22, 18, 4, 22, 22
%e 22, 19, 5, 23, 23
%e 24, 24, 24, 0, 24
%e ...
%o (Scheme)
%o (define (A275730 n) (A275730bi (A002262 n) (A025581 n)))
%o (define (A275730bi n c) (let loop ((z 0) (n n) (m 2) (f 1) (c c)) (let ((d (modulo n m))) (cond ((zero? n) z) ((zero? c) (loop z (/ (- n d) m) (+ 1 m) (* f m) (- c 1))) (else (loop (+ z (* f d)) (/ (- n d) m) (+ 1 m) (* f m) (- c 1)))))))
%Y Transpose: A275731.
%Y Column 0: A052928, Main diagonal: A001477.
%Y Cf. A084558, A257687.
%Y Can be used when computing A275732 and A275736.
%K nonn,base,tabl
%O 0,6
%A _Antti Karttunen_, Aug 08 2016
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