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%I M0178 #33 May 05 2018 02:23:49
%S 0,1,2,1,6,3,1,5,3,2,1,2,3,4,3,1,9,3,6,7,8,1,10,3,2,3,4,5,1,4,3,8,7,5,
%T 9,7,1,14,3,4,7,4,2,9,4,1,2,3,4,7,8,12,16,9,3,1,12,3,14,7,6,4,8,6,3,2,
%U 1,6,3,5,7,11,4
%N Remoteness number of n in Simon Norton's game of Tribulations.
%C The game of Tribulations is similar to Epstein's game in A005240, but the number of chips to be put or taken is the largest triangular number not larger than C: C-> C +- A057944(C). The remoteness is the number of moves in the game if the initial heap has n chips and both players play the optimum strategy. - _R. J. Mathar_, May 06 2016
%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 502.
%D R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 88.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. J. Mathar, <a href="/A006019/b006019.txt">Table of n, a(n) for n = 0..9999</a>
%H R. J. Mathar, <a href="/A006019/a006019.java.txt">JAVA Program calculating A006019</a>
%e For all positive triangular numbers (A000217) the remoteness is 1, because the starting player uses the strategy to take all of the chips and the game is over. The remoteness of 2 is 2, because taking one or putting one in the first move leads anyway to a n with remoteness 1. The remoteness of 4 is 6: 4 -> 7 -> 13 -> 23 -> 2 -> (1 or 3) -> 0. - _R. J. Mathar_, May 06 2016
%Y See A266726 for indices of even-valued terms (losing positions).
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E Name and offset corrected by _N. J. A. Sloane_, Jan 03 2016
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