A037988 Critical values in Conway's game of one-dimensional phutball.

1, 3, 4, 7, 9, 10, 11, 15, 16, 19, 21, 23, 24, 25, 26, 31, 33, 34, 35, 39, 40, 43, 44, 47, 49, 51, 53, 54, 55, 56, 57, 63, 64, 67, 69, 71, 72, 73, 74, 79, 81, 82, 83, 87, 89, 90, 91, 95, 96, 99, 100, 103, 104, 107, 109, 111, 113, 115, 116

Offset: 0

Author

Erich Friedman

Keywords

• easy
• nonn

Comments

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.

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

Conjectured partial sums of A272729 (true for at least 8192 terms). - Sean A. Irvine, Jun 26 2022

References

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

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A272729.