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
Examples
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
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
Programs
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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 *) -
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))))))
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.
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