A278492 Square array where row n (n >= 0) gives the numbers remaining after the n-th round of the Flavius sieve, read by descending antidiagonals.

1, 2, 1, 3, 3, 1, 4, 5, 3, 1, 5, 7, 7, 3, 1, 6, 9, 9, 7, 3, 1, 7, 11, 13, 13, 7, 3, 1, 8, 13, 15, 15, 13, 7, 3, 1, 9, 15, 19, 19, 19, 13, 7, 3, 1, 10, 17, 21, 25, 25, 19, 13, 7, 3, 1, 11, 19, 25, 27, 27, 27, 19, 13, 7, 3, 1, 12, 21, 27, 31, 31, 31, 27, 19, 13, 7, 3, 1, 13, 23, 31, 37, 39, 39, 39, 27, 19, 13, 7, 3, 1

Offset: 0

Author

Antti Karttunen, Nov 23 2016, after David W. Wilson's posting on SeqFan-list Nov 22 2016

Keywords

• nonn
• tabl

Comments

The terms of square array A(row,col) are read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

Examples

			The top left corner of the array:
1, 2, 3,  4,  5,  6,  7,  8,  9, 10 (row 0: start from A000027)
1, 3, 5,  7,  9, 11, 13, 15, 17, 19 (after the 1st round, A005408 remain)
1, 3, 7,  9, 13, 15, 19, 21, 25, 27 (after the 2nd, A047241)
1, 3, 7, 13, 15, 19, 25, 27, 31, 37
1, 3, 7, 13, 19, 25, 27, 31, 39, 43
1, 3, 7, 13, 19, 27, 31, 39, 43, 49
1, 3, 7, 13, 19, 27, 39, 43, 49, 61
1, 3, 7, 13, 19, 27, 39, 49, 61, 63
1, 3, 7, 13, 19, 27, 39, 49, 63, 67
1, 3, 7, 13, 19, 27, 39, 49, 63, 79
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of the array
• D. Wilson et al., Interesting sequence, SeqFan list, Nov. 2016
• Index entries for sequences generated by sieves
• Index entries for sequences related to the Josephus Problem

Crossrefs

One more than A278482.

Transpose: A278493.

Rows: A000027, A005408, A047241, A056530, A056531.

Main diagonal: A000960.

Cf. A278507 (the numbers removed at each round).

Similarly constructed arrays for other sieves: A258207, A260717.

Programs

Scheme

(define (A278492 n) (A278492bi (A002262 n) (A025581 n)))
(define (A278492bi row col) (+ 1 (A278482bi row col)))

Formula

A(n,k) = 1 + A278482(n,k).