A275730 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.

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, 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, 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

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array

Index entries for sequences related to factorial base representation

Formula

Other identities:

For all n >= 1, A(n,A084558(n)-1) = A257687(n).

For all n >= 0, A(n,A084558(n)) = n.

Example

Columns 0-4 of rows 0 - 24 of the array:
  0, 0, 0, 0, 0, ... [No matter which digit of zero we clear, it stays zero forever]
  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]
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].
  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].
  4, 0, 4, 4, 4
  4, 1, 5, 5, 5
  6, 6, 0, 6, 6
  6, 7, 1, 7, 7
  8, 6, 2, 8, 8
  8, 7, 3, 9, 9
  10, 6, 4, 10, 10
  10, 7, 5, 11, 11
  12, 12, 0, 12, 12
  12, 13, 1, 13, 13
  14, 12, 2, 14, 14
  14, 13, 3, 15, 15
  16, 12, 4, 16, 16
  16, 13, 5, 17, 17
  18, 18, 0, 18, 18
  18, 19, 1, 19, 19
  20, 18, 2, 20, 20
  20, 19, 3, 21, 21
  22, 18, 4, 22, 22
  22, 19, 5, 23, 23
  24, 24, 24, 0, 24
  ...

Prog

(Scheme)
(define (A275730 n) (A275730bi (A002262 n) (A025581 n)))
(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)))))))

Crossrefs

Transpose: A275731.

Column 0: A052928, Main diagonal: A001477.

Cf. A084558, A257687.

Can be used when computing A275732 and A275736.

Sequence in context: A309011 A365921 A086713 * A049771 A352514 A158944

Adjacent sequences: A275727 A275728 A275729 * A275731 A275732 A275733

Keyword

nonn,base,tabl

Author

Antti Karttunen, Aug 08 2016

Status

approved