The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083044

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A083044

Square table read by antidiagonals forms a permutation of the natural numbers: T(n,0) = floor(n*x/(x-1))+1, T(n,k+1) = ceiling(x*T(n,k)), where x=3/2, n >= 0, k >= 0.
(history; published version)

#36 by N. J. A. Sloane at Wed Aug 28 10:58:04 EDT 2024

STATUS

proposed

approved

#35 by Glen Whitney at Tue Aug 27 17:56:12 EDT 2024

STATUS

editing

proposed

#34 by Glen Whitney at Tue Aug 27 17:55:27 EDT 2024

COMMENTS

Consider the following two-player game: Start with two nonempty piles of counters. Players alternate taking turns consisting of first discarding one of the piles and then dividing the remaining pile into two nonempty piles. The smaller pile may always be discarded; the larger pile may only be discarded if the smaller pile is at least half as large. (Either pile may be discarded if they are equal.) The player who cannot move (because the configuration has reached two piles of one counter each) loses. Then the numbers c for which two piles of size c is a losing configuration (for the player whose turn it is) are exactly T(4,k) for k > 1, together with 1,3,5, and 9. - Glen Whitney, Aug 03 2018

STATUS

approved

editing

Discussion

Tue Aug 27

17:56

Glen Whitney: A colleague pointed out that the description of the pile game was slightly incomplete.

#33 by Peter Luschny at Fri Aug 07 01:46:04 EDT 2020

STATUS

reviewed

approved

#32 by Hugo Pfoertner at Fri Aug 07 01:13:12 EDT 2020

STATUS

proposed

reviewed

#31 by Peter Munn at Mon Aug 03 10:50:17 EDT 2020

STATUS

editing

proposed

#30 by Peter Munn at Mon Aug 03 10:49:51 EDT 2020

FORMULA

aT(A163491(n)-1, A087088(n)-1) = n. - Peter Munn, Jul 16 2020 [corrected Peter Munn, Aug 02 2020]

STATUS

proposed

editing

#29 by Peter Munn at Sun Aug 02 13:20:49 EDT 2020

STATUS

editing

proposed

Discussion

Sun Aug 02

13:22

Michel Marcus: you mean T(A163491(n)-1, A087088(n)-1) = n  ?

Mon Aug 03

10:47

Peter Munn: Yes (and the OEIS notification of your comment seems to have fallen foul of a filter beyond my control, so I've only just seen your question.)

#28 by Peter Munn at Sun Aug 02 13:18:00 EDT 2020

FORMULA

a(A163491(n)-1), , A087088(n)-1)) = n. - Peter Munn, Jul 16 2020 [corrected _Peter Munn_, Aug 02 2020]

STATUS

approved

editing

Discussion

Sun Aug 02

13:19

Peter Munn: misplaced parentheses

#27 by Bruno Berselli at Thu Jul 16 08:34:39 EDT 2020

STATUS

reviewed

approved