A278505 Square array constructed from Flavius sieve: Each row n (n >= 1) starts with A000960(n), followed by all numbers removed at the stage n of the sieve.

1, 2, 3, 4, 5, 7, 6, 11, 9, 13, 8, 17, 21, 15, 19, 10, 23, 33, 37, 25, 27, 12, 29, 45, 55, 51, 31, 39, 14, 35, 57, 75, 85, 73, 43, 49, 16, 41, 69, 97, 111, 121, 99, 61, 63, 18, 47, 81, 115, 145, 159, 151, 127, 67, 79, 20, 53, 93, 135, 171, 199, 211, 193, 163, 87, 91, 22, 59, 105, 157, 205, 243, 267, 271, 247, 187, 103, 109

Offset: 1

Author

Antti Karttunen, Nov 23 2016

Keywords

• nonn
• 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), ...

Examples

			The top left corner of the array:
   1,  2,   4,   6,   8,  10,  12,  14,  16,  18
   3,  5,  11,  17,  23,  29,  35,  41,  47,  53
   7,  9,  21,  33,  45,  57,  69,  81,  93, 105
  13, 15,  37,  55,  75,  97, 115, 135, 157, 175
  19, 25,  51,  85, 111, 145, 171, 205, 231, 265
  27, 31,  73, 121, 159, 199, 243, 283, 327, 367
  39, 43,  99, 151, 211, 267, 319, 379, 433, 487
  49, 61, 127, 193, 271, 343, 421, 483, 559, 631
  63, 67, 163, 247, 339, 427, 519, 607, 691, 793
  79, 87, 187, 303, 403, 523, 639, 739, 853, 963
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences generated by sieves
• Index entries for sequences related to the Josephus Problem

Crossrefs

Inverse: A278506.

Transpose: A278503.

Column 1: A000960, column 2: A100287 (apart from its initial 1), A099259 (differences).

Cf. A278538 (row index of n), A278539 (column index of n).

Cf. also arrays A278507 and A278511 (different variants).

Cf. also A255545 (an analogous array constructed for Lucky sieve).

Programs

Scheme

(define (A278505 n) (A278505bi (A002260 n) (A004736 n)))
(define (A278505bi row col) (if (= 1 col) (A000960 row) (A278507bi row (- col 1)))) ;; Code for A278507bi given in A278507.

Formula

A(row,1) = A000960(row); for col > 1, A(row,col) = A278507(row,col-1).

For all n >= 1, A(A278538(n), A278539(n)) = n.