A276955 Square array A(row,col): A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1)); Dispersion of factorial base left shift A153880.

1, 2, 3, 6, 8, 4, 24, 30, 12, 5, 120, 144, 48, 14, 7, 720, 840, 240, 54, 26, 9, 5040, 5760, 1440, 264, 126, 32, 10, 40320, 45360, 10080, 1560, 744, 150, 36, 11, 362880, 403200, 80640, 10800, 5160, 864, 168, 38, 13, 3628800, 3991680, 725760, 85680, 41040, 5880, 960, 174, 50, 15, 39916800, 43545600, 7257600, 766080, 367920, 46080, 6480, 984, 246, 56, 16

Offset: 1

Author

Antti Karttunen, Sep 22 2016

Keywords

• nonn
• base
• tabl

Comments

The square array A(row,col) is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

When viewed in factorial base (A007623) the terms on each row start all with the same prefix, but with an increasing number of zeros appended to the end. For example, for row 8 (A001344 from a(1)=11 onward), the terms written in factorial base look as: 121, 1210, 12100, 121000, ...

Examples

			The top left {1..9} x {1..18} corner of the array:
   1,  2,   6,   24,   120,    720,    5040,    40320,    362880
   3,  8,  30,  144,   840,   5760,   45360,   403200,   3991680
   4, 12,  48,  240,  1440,  10080,   80640,   725760,   7257600
   5, 14,  54,  264,  1560,  10800,   85680,   766080,   7620480
   7, 26, 126,  744,  5160,  41040,  367920,  3669120,  40279680
   9, 32, 150,  864,  5880,  46080,  408240,  4032000,  43908480
  10, 36, 168,  960,  6480,  50400,  443520,  4354560,  47174400
  11, 38, 174,  984,  6600,  51120,  448560,  4394880,  47537280
  13, 50, 246, 1464, 10200,  81360,  730800,  7297920,  80196480
  15, 56, 270, 1584, 10920,  86400,  771120,  7660800,  83825280
  16, 60, 288, 1680, 11520,  90720,  806400,  7983360,  87091200
  17, 62, 294, 1704, 11640,  91440,  811440,  8023680,  87454080
  18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400
  19, 74, 366, 2184, 15240, 121680, 1093680, 10926720, 120113280
  20, 78, 384, 2280, 15840, 126000, 1128960, 11249280, 123379200
  21, 80, 390, 2304, 15960, 126720, 1134000, 11289600, 123742080
  22, 84, 408, 2400, 16560, 131040, 1169280, 11612160, 127008000
  23, 86, 414, 2424, 16680, 131760, 1174320, 11652480, 127370880
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1830; the first 60 antidiagonals of array
• Index entries for sequences related to factorial base representation
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A276956.

Transpose: A276953.

Cf. A276949 (index of column where n appears), A276951 (index of row).

Cf. A153880.

Columns 1-3: A273670, A276932, A276933.

The following lists some of the rows that have their own entries. Pattern present in the factorial base expansion of the terms on that row is given in double quotes:

Row 1: A000142 (from a(1)=1, "1" onward),

Row 2: A001048 (from a(2)=3, "11" onward),

Row 3: A052849 (from a(2)=4, "20" onward).

Row 4: A052649 (from a(1)=5, "21" onward).

Row 5: A108217 (from a(3)=7, "101" onward).

Row 6: A054119 (from a(3)=9, "111" onward).

Row 7: A052572 (from a(2)=10, "120" onward).

Row 8: A001344 (from a(1)=11, "121" onward).

Row 13: A052560 (from a(3)=18, "300" onward).

Row 16: A225658 (from a(1)=21, "311" onward).

Row 20: A276940 (from a(3) = 27, "1011" onward).

Related or similar permutations: A257505, A275848, A273666.

Cf. also arrays A276617, A276588 & A276945.

Programs

Scheme

(define (A276955 n) (A276955bi (A002260 n) (A004736 n)))
(define (A276955bi row col) (if (= 1 col) (A273670 (- row 1)) (A153880 (A276955bi row (- col 1)))))

Formula

A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1))

As a composition of other permutations:

a(n) = A275848(A257505(n)).