

A006019


Remoteness number of n in Simon Norton's game of Tribulations.
(Formerly M0178)


3



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, 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, 1, 6, 3, 5, 7, 11, 4
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OFFSET

0,3


COMMENTS

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


REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 502.
R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 88.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

R. J. Mathar, Table of n, a(n) for n = 0..9999
R. J. Mathar, JAVA Program calculating A006019


EXAMPLE

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


CROSSREFS

See A266726 for indices of evenvalued terms (losing positions).
Sequence in context: A243484 A181811 A284431 * A201146 A065553 A016545
Adjacent sequences: A006016 A006017 A006018 * A006020 A006021 A006022


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Name and offset corrected by N. J. A. Sloane, Jan 03 2016


STATUS

approved



