A278507 Square array A(row,col) where row n lists the numbers removed in round n of Flavius sieve. Array is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

2, 4, 5, 6, 11, 9, 8, 17, 21, 15, 10, 23, 33, 37, 25, 12, 29, 45, 55, 51, 31, 14, 35, 57, 75, 85, 73, 43, 16, 41, 69, 97, 111, 121, 99, 61, 18, 47, 81, 115, 145, 159, 151, 127, 67, 20, 53, 93, 135, 171, 199, 211, 193, 163, 87, 22, 59, 105, 157, 205, 243, 267, 271, 247, 187, 103, 24, 65, 117, 175, 231, 283, 319, 343, 339, 303, 229, 123

Offset: 1

Author

Antti Karttunen, Nov 23 2016

Keywords

• nonn
• tabl

Examples

			The top left corner of the array:
   2,   4,   6,   8,  10,  12,  14,  16,  18,   20
   5,  11,  17,  23,  29,  35,  41,  47,  53,   59
   9,  21,  33,  45,  57,  69,  81,  93, 105,  117
  15,  37,  55,  75,  97, 115, 135, 157, 175,  195
  25,  51,  85, 111, 145, 171, 205, 231, 265,  291
  31,  73, 121, 159, 199, 243, 283, 327, 367,  409
  43,  99, 151, 211, 267, 319, 379, 433, 487,  547
  61, 127, 193, 271, 343, 421, 483, 559, 631,  699
  67, 163, 247, 339, 427, 519, 607, 691, 793,  879
  87, 187, 303, 403, 523, 639, 739, 853, 963, 1081
		

Links

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

Crossrefs

Transpose: A278508.

This is array A278505 without its leftmost column, A000960.

Column 1: A100287 (apart from its initial 1).

Rows: A005843, A016969, A017629.

Cf. A278529 (column index of n), A278538 (row index of n).

Cf. A278492.

Cf. A255543 for analogous array for Lucky sieve.

Programs

Scheme

(define (A278507 n) (A278507bi (A002260 n) (A004736 n)))
(define (A278507bi row col) (cond ((= 1 row) (* 2 col)) (else (A278492bi (- row 1) (+ -1 (* col (+ 1 row)))))))
;; Code for A278492bi given in A278492.

Formula

A(1,col) = 2*col; for row > 1, A(row,col) = A278492(row-1,(col*(row+1))-1). [Note that unlike this array, A278492 uses zero-based indexing for its rows and columns.]