A006019 - OEIS

A006019

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

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

(list; graph; refs; listen; history; text; internal format)

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 even-valued terms (losing positions).

Sequence in context: A333078 A352376 A337470 * 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