

A161000


Triangle read by rows: For 1 <= m <= n, t(n,m) = the smallest positive integer that when read in binary contains exactly (n+1m) 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



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
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OFFSET

1,2


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.


LINKS

Table of n, a(n) for n=1..34.


EXAMPLE

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.
Sequence in context: A099438 A002178 A013558 * A220363 A120078 A096201
Adjacent sequences: A160997 A160998 A160999 * A161001 A161002 A161003


KEYWORD

base,nonn,tabl


AUTHOR

Leroy Quet, Jun 01 2009


EXTENSIONS

Extended by Ray Chandler, Jun 13 2009


STATUS

approved



