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A359807
a(1) = 0; thereafter a(n) is the largest a(i) + i which is < n among i = 1..n-1.
4
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
1,4
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.
LINKS
EXAMPLE
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.
PROG
(PARI) lista(nn) = my(va = vector(nn)); va[1] = 0; for (n=2, nn, va[n] = vecmax(select(x->(x<n), vector(n-1, i, va[i]+i))); ); va; \\ Michel 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
CROSSREFS
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Jan 13 2023
STATUS
approved