A278482 -id:A278482 - cp's OEIS frontend

A278483 Transpose of square array A278482.

0, 0, 1, 0, 2, 2, 0, 2, 4, 3, 0, 2, 6, 6, 4, 0, 2, 6, 8, 8, 5, 0, 2, 6, 12, 12, 10, 6, 0, 2, 6, 12, 14, 14, 12, 7, 0, 2, 6, 12, 18, 18, 18, 14, 8, 0, 2, 6, 12, 18, 24, 24, 20, 16, 9, 0, 2, 6, 12, 18, 26, 26, 26, 24, 18, 10, 0, 2, 6, 12, 18, 26, 30, 30, 30, 26, 20, 11, 0, 2, 6, 12, 18, 26, 38, 38, 38, 36, 30, 22, 12

Offset: 0

Antti Karttunen, Nov 23 2016

See comments in A278482.

Antti Karttunen, Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of the array

Transpose: A278482.

(define (A278483 n) (A278482bi (A025581 n) (A002262 n))) ;; Code for A278482bi given in A278482.

A278484 Main diagonal of A278482.

Original entry on oeis.org

0, 2, 6, 12, 18, 26, 38, 48, 62, 78, 90, 108, 132, 146, 180, 206, 222, 252, 288, 306, 348, 386, 398, 458, 480, 528, 566, 612, 648, 708, 762, 806, 842, 926, 948, 1008, 1092, 1110, 1188, 1260, 1320, 1358, 1470, 1482, 1578, 1692, 1718, 1806, 1898, 1932, 2022, 2160, 2186, 2268, 2366, 2478, 2532, 2702, 2738, 2798, 2966, 3018

Offset: 0

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

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10000
D. Wilson et al., Interesting sequence, SeqFan list, Nov. 2016
Index entries for sequences generated by sieves

Cf. A000960, A073359.
Main diagonal of A278482 (and A278483).
Partial sums of A278484.

a[n_]:= Fold[Floor@Times@##&,Prepend[Table[(k + 1)/k, {k, n, 1, -1}], n]] (* Ethan Beihl, Nov 29 2016 *)

By definition, a(n) = A278482(n,n).
a(n) = A000960(n + 1) - 1.
a(n) = 2*A073359(n). [Observed by Arie Groeneveld on SeqFan list, Nov 22 2016.] [Conjectural, true for n <= 2000 David W. Wilson, Nov 23 2016]

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.

Original entry on oeis.org

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

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

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), ...

			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

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

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.

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

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

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A278483 Transpose of square array A278482.

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A278484 Main diagonal of A278482.

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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.

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