A278482 Square array A(n,k): A(0, n) = n; A(k, n) = A(k-1, floor(n*(k+1)/k)), for k >= 1, read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

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

Offset

0,4

Comments

Related to Flavius Josephus's sieve. See A278492 and the postings by David W. Wilson et al. on SeqFan list, Nov 22 2016.

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(0, n) = n for n >= 0; A(k, n) = A(k - 1, [n*(k + 1)/k]) for k > 0 and n >= 0. Here [ ] stands for floor-function. From David W. Wilson's posting to SeqFan list on 22 Nov 2016.

Example

The top left corner of the array:
  0, 1, 2,  3,  4,  5,  6,  7,  8,  9
  0, 2, 4,  6,  8, 10, 12, 14, 16, 18
  0, 2, 6,  8, 12, 14, 18, 20, 24, 26
  0, 2, 6, 12, 14, 18, 24, 26, 30, 36
  0, 2, 6, 12, 18, 24, 26, 30, 38, 42
  0, 2, 6, 12, 18, 26, 30, 38, 42, 48
  0, 2, 6, 12, 18, 26, 38, 42, 48, 60
  0, 2, 6, 12, 18, 26, 38, 48, 60, 62
  0, 2, 6, 12, 18, 26, 38, 48, 62, 66
  0, 2, 6, 12, 18, 26, 38, 48, 62, 78

Mathematica

t[k_, n_] := t[k - 1, Floor[n*(k + 1)/k]]; t[0, n_] = n; Table[t[k - 1, n - k + 1], {n, 0, 12}, {k, 1, n + 1}] // Flatten (* Robert G. Wilson v, Nov 23 2016 *)

Prog

(Scheme)
(define (A278482 n) (A278482bi (A002262 n) (A025581 n)))
(define (A278482bi row col) (if (zero? row) col (A278482bi (- row 1) (floor->exact (* col (/ 1 row) (+ 1 row))))))

Crossrefs

Transpose: A278483.

Main diagonal: A278484.

One less than A278492.

Sequence in context: A300453 A239292 A262879 * A324657 A369524 A339422

Adjacent sequences: A278479 A278480 A278481 * A278483 A278484 A278485

Keyword

nonn,tabl

Author

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

Status

approved