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.

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

Author

Antti Karttunen, Sep 24 2016

Keywords

• nonn
• base
• tabl

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

Examples

			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
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..630; the first 35 antidiagonals of array
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences related to primorial base

Crossrefs

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.

Programs

Scheme

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

Formula

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