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

2,9

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.

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

Example

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

Prog

(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.

Crossrefs

Cf. A003309, A255127, A272565, A276570.

Column 1, Rows 1 & 2: A000004.

Column 2: A276576.

Row 5: A276577.

Sequence in context: A287287 A323519 A333979 * A331437 A351572 A108708

Adjacent sequences: A276577 A276578 A276579 * A276581 A276582 A276583

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 13 2016

Status

approved