A286615 -id:A286615 - cp's OEIS frontend

A286616 Transpose of square array A286615.

0, 2, 1, 3, 7, 5, 4, 11, 35, 29, 6, 13, 59, 239, 209, 8, 31, 65, 419, 2519, 2309, 9, 37, 215, 449, 4619, 32339, 30029, 10, 41, 245, 2339, 4829, 60059, 540539, 510509, 12, 43, 269, 2549, 30239, 62369, 1021019, 10210199, 9699689, 14, 61, 275, 2729, 32549, 512819, 1051049, 19399379, 232792559, 223092869

Offset: 1

Antti Karttunen, Jun 30 2017

A permutation of nonnegative integers.

			The top left 7 X 7 corner of the array:
      0,      2,       3,       4,       6,        8,        9
      1,      7,      11,      13,      31,       37,       41
      5,     35,      59,      65,     215,      245,      269
     29,    239,     419,     449,    2339,     2549,     2729
    209,   2519,    4619,    4829,   30239,    32549,    34649
   2309,  32339,   60059,   62369,  512819,   542849,   570569
  30029, 540539, 1021019, 1051049, 9729719, 10240229, 10720709

Transpose: A286615.
One less than A276943.
Column 1: A057588.

(define (A286616 n) (A286615bi (A004736 n) (A002260 n))) ;; For the rest, see under A286615, A276945, etc.

A(n,k) = A286615(k,n) = A276943(n,k)-1.

A276945 Square array A(row,col): A(row,1) = A276155(row), and for col > 1, A(row,col) = A276154(A(row,col-1)); Dispersion of primorial base left shift A276154.

Original entry on oeis.org

1, 2, 3, 6, 8, 4, 30, 36, 12, 5, 210, 240, 60, 14, 7, 2310, 2520, 420, 66, 32, 9, 30030, 32340, 4620, 450, 216, 38, 10, 510510, 540540, 60060, 4830, 2340, 246, 42, 11, 9699690, 10210200, 1021020, 62370, 30240, 2550, 270, 44, 13, 223092870, 232792560, 19399380, 1051050, 512820, 32550, 2730, 276, 62, 15

Offset: 1

Antti Karttunen, Sep 24 2016

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 in column k are all multiples of A002110(k-1). Dividing that factor out gives array A286625. - Antti Karttunen, Jun 30 2017

			The top left corner of the array:
   1,  2,   6,   30,   210,    2310,    30030,    510510
   3,  8,  36,  240,  2520,   32340,   540540,  10210200
   4, 12,  60,  420,  4620,   60060,  1021020,  19399380
   5, 14,  66,  450,  4830,   62370,  1051050,  19909890
   7, 32, 216, 2340, 30240,  512820,  9729720, 223603380
   9, 38, 246, 2550, 32550,  542850, 10240230, 233303070
  10, 42, 270, 2730, 34650,  570570, 10720710, 242492250
  11, 44, 276, 2760, 34860,  572880, 10750740, 243002760
  13, 62, 426, 4650, 60270, 1023330, 19429410, 446696250
  15, 68, 456, 4860, 62580, 1053360, 19939920, 456395940
  16, 72, 480, 5040, 64680, 1081080, 20420400, 465585120
  17, 74, 486, 5070, 64890, 1083390, 20450430, 466095630
  18, 90, 630, 6930, 90090, 1531530, 29099070, 669278610

Inverse permutation: A276946.
Transpose: A276943. One more than A286615.
Column 1: A276155.
Row 1: A002110.
Row 2: A276939.
Row 3: A088860 (2*A002110).
Row 11: 2*A276939 (row 2) from 16, 72, 480, 5040, 64680, ... onward.
Row 13: 3*A002110, from 18, 90, 630, 6930, 90090, ... onward.
Cf. A276154.
Cf. also arrays A286625, A276955.

(define (A276945 n) (A276945bi (A002260 n) (A004736 n)))
(define (A276945bi row col) (if (= 1 col) (A276155 row) (A276154 (A276945bi row (- col 1)))))

A(row,1) = A276155(row); for row > 1, A(row,col) = A276154(A(row,col-1)).

cp's OEIS Frontend

A286616 Transpose of square array A286615.

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