A034298 a(n) = min_S max_i b_i where S={b_i} (1 <= i <= n), b_i > 0, b_i distinct and either b_i|b_{i-1} or b_{i-1}|b_i.
1, 2, 3, 4, 6, 6, 8, 9, 10, 12, 12, 14, 15, 16, 18, 18, 20, 21, 22, 24, 24, 26, 27, 28, 30, 30, 32, 33, 35, 36, 39, 40, 42, 42, 44, 44, 45, 48, 48, 50, 50, 51, 52, 54, 55, 56, 57, 60, 60, 63, 64, 66, 66, 68, 69, 70, 70, 72, 75, 76, 77, 78, 78, 80, 81, 84, 87, 88
Offset: 1
Examples
For example, a(12)=14 because of {9, 3, 6, 12, 4, 8, 2, 10, 5, 1, 7, 14} and the fact that no sequence of 12 distinct positive integers < 14 has this division property.
a(32) = 40 because of {22, 11, 33, 3, 39, 13, 26, 2, 34, 17, 1, 10, 20, 40, 8, 16, 32, 4, 28, 14, 7, 35, 5, 15, 30, 6, 24, 12, 36, 18, 9, 27};
a(34) = 42 because of {22, 11, 33, 3, 39, 13, 26, 2, 34, 17, 1, 10, 20, 40, 8, 16, 32, 4, 28, 14, 42, 21, 7, 35, 5, 15, 30, 6, 24, 12, 36, 18, 9, 27};
a(37) = 45 because of {17, 34, 2, 38, 19, 1, 26, 13, 39, 3, 33, 11, 22, 44, 4, 16, 32, 8, 24, 6, 12, 36, 18, 9, 45, 15, 30, 10, 20, 40, 5, 35, 7, 21, 42, 14, 28}.
Links
- E. J. Friedman, Problem of the Month (November 1998), Math. Magic.
Extensions
a(31)-a(37) from Xavier Martres, Apr 26 2019
More terms from Jinyuan Wang, Aug 02 2022