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Critical values in Conway's game of one-dimensional phutball.
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%I #22 Jun 27 2022 04:37:51

%S 1,3,4,7,9,10,11,15,16,19,21,23,24,25,26,31,33,34,35,39,40,43,44,47,

%T 49,51,53,54,55,56,57,63,64,67,69,71,72,73,74,79,81,82,83,87,89,90,91,

%U 95,96,99,100,103,104,107,109,111,113,115,116

%N Critical values in Conway's game of one-dimensional phutball.

%C The first player can move the ball 2*a(n) spaces before the second player can move the ball 2*(a(n-1) + 1) spaces.

%C A self-describing sequence. Pick any number n; this n says: "There are n terms in the sequence which are <= 2n". This sequence is the slowest increasing one with this property. - _Eric Angelini_, Jun 15 2007

%C Conjectured partial sums of A272729 (true for at least 8192 terms). - _Sean A. Irvine_, Jun 26 2022

%D Berlekamp, Conway and Guy, "Winning Ways", Volume 2. Academic Press, 1982

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a037/A037988.java">Java program</a> (github)

%Y Cf. A272729.

%K easy,nonn

%O 0,2

%A _Erich Friedman_