A161000 Triangle read by rows: For 1 <= m <= n, t(n,m) = the smallest positive integer that when read in binary contains exactly (n+1-m) runs of 0's and 1's, all runs being of distinct lengths m through n in any order within binary t(n,m).

1, 4, 3, 35, 24, 7, 536, 391, 112, 15, 16775, 12400, 3599, 480, 31, 1060976, 790031, 229856, 30751, 1984, 63, 135007759, 100893152, 29390879, 3934144, 254015, 8064, 127, 34460631520, 25799194655, 7520126912, 1006886975, 65019776, 2064511

Offset: 1

Author

Leroy Quet, Jun 01 2009

Keywords

• base
• nonn
• tabl

Comments

Think of binary n as a string S of 0's and 1's. By a "run" of 0's or 1's, it is meant either a substring all of contiguous 0's, each run bounded by 1's or the edge of S; or a substring all of contiguous 1's, each run bounded by 0's or the edge of S.

Examples

			The terms of the first few rows of the triangle converted to binary:
1
100, 11
100011, 11000, 111
1000011000, 110000111, 1110000, 1111
Note that all terms in row n have a run with n 0s or 1's (and no run of more 0's or 1s), and all terms in column m have a run of m 0's or 1's (but no run of fewer 0's or 1's). Each length of run occurs exactly once in each binary number.
		

Crossrefs

Cf. A161001.

Extensions

Extended by Ray Chandler, Jun 13 2009