A278492 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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), ...

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

FORMULA

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

EXAMPLE

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

PROG

(Scheme)

(define (A278492 n) (A278492bi (A002262 n) (A025581 n)))

(define (A278492bi row col) (+ 1 (A278482bi row col)))

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.

Sequence in context: A188002 A186974 A286312 * A128139 A208721 A208777

Adjacent sequences: A278489 A278490 A278491 * A278493 A278494 A278495

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved