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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A129688 A309011 A086713 * A049771 A158944 A156663

Adjacent sequences:  A275727 A275728 A275729 * A275731 A275732 A275733

KEYWORD

nonn,base,tabl

AUTHOR

Antti Karttunen, Aug 08 2016

STATUS

approved

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Last modified January 26 12:05 EST 2022. Contains 350598 sequences. (Running on oeis4.)