A359807 a(1) = 0; thereafter a(n) is the largest a(i) + i which is < n among i = 1..n-1.

0, 1, 1, 3, 4, 4, 4, 7, 7, 9, 10, 11, 11, 11, 11, 15, 16, 16, 16, 19, 19, 21, 21, 23, 24, 25, 26, 26, 26, 26, 26, 31, 31, 33, 34, 35, 35, 35, 35, 39, 40, 40, 40, 43, 44, 44, 44, 47, 47, 49, 49, 51, 51, 53, 54, 55, 56, 57, 57, 57, 57, 57, 57, 63, 64, 64, 64, 67, 67, 69, 69, 71, 72, 73, 74, 74, 74, 74, 74

Offset: 1

Author

Neal Gersh Tolunsky, Jan 13 2023

Keywords

• nonn

Comments

Critical values of Conway's game of one-dimensional phutball (A037988), except for the initial zero.

Conjectured run lengths are A272729, and the terms which occur here are partial sums of A272729.

The next distinct term here occurs at index a(i)+i+1 for every index i.

Examples

			For n=3, we see that for i=1 and 2, a(i)+i = 1 and 3, of which only 1 is < n=3, so that a(3)=1.
For n=5, i=1..4 have a(i)+i = 1,3,4,7 and the largest < n=5 is 4 so that a(5)=4.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A367039, A037988, A272729, A272727, A094591, A367026.

Programs

PARI

lista(nn) = my(va = vector(nn)); va[1] = 0; for (n=2, nn, va[n] = vecmax(select(x->(xMichel Marcus, Jan 31 2023

PARI

{ my (v = 0, m = 0); for (n = 1, 79, if (bittest(m, n-1), v = n-1); print1 (v", "); m = bitor(m, 2^(v+n))) } \\ Rémy Sigrist, Feb 08 2023