A276580 Square array A(n,k) = A276570(A255127(n,k)), numbers in Ludic array reduced by the first element of each row. Array is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, 1, 4, 8, 0, 0, 0, 4, 1, 8, 3, 16, 0, 0, 0, 0, 4, 5, 2, 0, 7, 0, 0, 0, 4, 2, 9, 3, 9, 18, 17, 0, 0, 0, 0, 2, 2, 0, 10, 12, 11, 2, 0, 0, 0, 4, 0, 2, 8, 2, 17, 7, 23, 31, 0, 0, 0, 0, 3, 6, 7, 3, 11, 24, 0, 6, 6, 0, 0, 0, 4, 3, 3, 4, 0, 22, 20, 23, 10, 30, 16, 0

Offset: 2

Author

Antti Karttunen, Sep 13 2016

Keywords

• nonn
• tabl

Comments

The starting offset of the sequence giving the terms of square array is 2, to tally with the indexing used in A255127. The row and column indices both start from 1.

Row 4 seems to have a period of 8: [0, 3, 3, 1, 1, 4, 2, 2], while row 5 (A276577) seems to have a period of 48.

Examples

			The top left 17 x 15 corner of the array:
   n   A003309(n+1) = A255127(n,1).
   |   |
   |   | |           A255127(n,k) modulo A003309(n+1)
   v   v |
   1   2 |0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   2   3 |0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   3   5 |0,  4,  0,  4,  0,  4,  0,  4,  0,  4,  0,  4,  0,  4,  0,  4,  0
   4   7 |0,  3,  3,  1,  1,  4,  2,  2,  0,  3,  3,  1,  1,  4,  2,  2,  0
   5  11 |0,  0,  4,  8,  5,  9,  2,  2,  6,  3,  7,  0,  4,  4,  1,  5,  9
   6  13 |0,  8,  3,  2,  3,  0,  8,  7,  4, 12,  4, 12,  7,  4,  3, 11, 12
   7  17 |0, 16,  0,  9, 10,  2,  3,  0,  7, 10,  0,  3,  8, 13, 12,  0,  5
   8  23 |0,  7, 18, 12, 17, 11, 22, 14,  2,  7,  1, 14,  2, 17,  7, 18, 10
   9  25 |0, 17, 11,  7, 24, 20,  8,  8,  6, 21, 19, 15,  3,  3, 16, 16, 14
  10  29 |0,  2, 23,  0, 23, 25,  0, 25,  0, 25,  2,  2,  0,  2,  6,  8,  8
  11  37 |0, 31,  6, 10, 30, 36,  3, 21, 17, 29, 16, 14, 22, 34,  1, 13, 27
  12  41 |0,  6, 30, 38, 25, 37,  4, 16,  5, 21,  0, 12, 22, 40, 29,  6, 24
  13  43 |0, 16, 42,  9, 35, 38,  7, 31,  8,  1, 25,  6, 24,  5, 35, 26,  1
  14  47 |0, 26, 13, 45, 32, 23, 10, 40, 19, 14, 21,  8, 28, 15,  0, 40, 25
  15  53 |0, 42, 31, 14, 11,  0,  1,  0, 50, 31, 20, 29, 12, 11, 20,  1, 51
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of array
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003309, A255127, A272565, A276570.

Column 1, Rows 1 & 2: A000004.

Column 2: A276576.

Row 5: A276577.

Programs

Scheme

(define (A276580 n) (A276580bi (A002260 (- n 1)) (A004736 (- n 1))))
(define (A276580bi row col) (A276570 (A255127bi row col))) ;; Code for A255127bi given in A255127.