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

1,2

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), ...

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

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.

Example

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

Prog

(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.

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).

Sequence in context: A369281 A266637 A370496 * A278506 A255546 A358874

Adjacent sequences: A278502 A278503 A278504 * A278506 A278507 A278508

Keyword

nonn,tabl

Author

Antti Karttunen, Nov 23 2016

Status

approved