A257503 Square array A(row,col) read by antidiagonals: A(1,col) = A256450(col-1), and for row > 1, A(row,col) = A255411(A(row-1,col)); Dispersion of factorial base shift A255411 (array transposed).

1, 2, 4, 3, 12, 18, 5, 16, 72, 96, 6, 22, 90, 480, 600, 7, 48, 114, 576, 3600, 4320, 8, 52, 360, 696, 4200, 30240, 35280, 9, 60, 378, 2880, 4920, 34560, 282240, 322560, 10, 64, 432, 2976, 25200, 39600, 317520, 2903040, 3265920, 11, 66, 450, 3360, 25800, 241920, 357840, 3225600, 32659200, 36288000, 13, 70, 456, 3456, 28800, 246240, 2540160, 3588480, 35925120, 399168000, 439084800

Offset: 1

Author

Antti Karttunen, Apr 27 2015

Keywords

• nonn
• base
• tabl

Comments

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

The first row (A256450) contains all the numbers which have at least one 1-digit in their factorial base representation (see A007623), after which the successive rows are obtained from the terms on the row immediately above by shifting their factorial representation one left and then incrementing the nonzero digits in that representation with a factorial base shift-operation A255411.

Examples

			The top left corner of the array:
     1,     2,     3,     5,      6,      7,      8,      9,     10,     11,     13
     4,    12,    16,    22,     48,     52,     60,     64,     66,     70,     76
    18,    72,    90,   114,    360,    378,    432,    450,    456,    474,    498
    96,   480,   576,   696,   2880,   2976,   3360,   3456,   3480,   3576,   3696
   600,  3600,  4200,  4920,  25200,  25800,  28800,  29400,  29520,  30120,  30840
  4320, 30240, 34560, 39600, 241920, 246240, 272160, 276480, 277200, 281520, 286560
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of array
• Index entries for sequences related to factorial base representation
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Transpose: A257505.

Inverse permutation: A257504.

Row index: A257679, Column index: A257681.

Row 1: A256450, Row 2: A257692, Row 3: A257693.

Columns 1-3: A001563, A062119, A130744 (without their initial zero-terms).

Column 4: A213167 (without the initial one).

Column 5: A052571 (without initial zeros).

Cf. A007623, A256450, A255411.

Cf. also permutations A255565 and A255566.

Thematically similar arrays: A083412, A135764, A246278.

Programs

Scheme

(define (A257503 n) (A257503bi (A002260 n) (A004736 n)))
(define (A257503bi row col) (if (= 1 row) (A256450 (- col 1)) (A255411 (A257503bi (- row 1) col))))

Formula

A(1,col) = A256450(col-1), and for row > 1, A(row,col) = A255411(A(row-1,col)).

Extensions

Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016