A276953 Square array A(row,col) read by antidiagonals: A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col)); Dispersion of factorial base shift A153880 (array transposed).

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

Offset

1,2

Comments

The 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.

Entries on row n are all multiples of n!. Dividing that factor out gives another array A276616.

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

Formula

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

As a composition of other permutations:

a(n) = A275848(A257503(n)).

Other identities. For all n >= 1:

A(A276949(n),A276951(n)) = n.

Example

The top left corner of the array:
    1,    3,     4,     5,     7,     9,    10,    11,    13,    15,    16
    2,    8,    12,    14,    26,    32,    36,    38,    50,    56,    60
    6,   30,    48,    54,   126,   150,   168,   174,   246,   270,   288
   24,  144,   240,   264,   744,   864,   960,   984,  1464,  1584,  1680
  120,  840,  1440,  1560,  5160,  5880,  6480,  6600, 10200, 10920, 11520
  720, 5760, 10080, 10800, 41040, 46080, 50400, 51120, 81360, 86400, 90720

Prog

(Scheme)
(define (A276953 n) (A276953bi (A002260 n) (A004736 n)))
(define (A276953bi row col) (if (= 1 row) (A273670 (- col 1)) (A153880 (A276953bi (- row 1) col))))

Crossrefs

Inverse permutation: A276954.

Transpose: A276955.

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

Cf. A153880, A273670.

Row 1: A273670, Row 2: A276932, Row 3: A276933.

Column 1: A000142. For other columns, see the rows of transposed array A276955.

Related or similar permutations: A257503, A275848, A273666.

Cf. also arrays A276616, A276589 & A276943.

Sequence in context: A082228 A114650 A170949 * A276943 A303148 A228784

Adjacent sequences: A276950 A276951 A276952 * A276954 A276955 A276956

Keyword

nonn,base,tabl

Author

Antti Karttunen, Sep 22 2016

Status

approved