A131094 Triangle where n-th row contains the smallest n positive integers (listed in order) with exactly n nonleading 0's in their binary representations.

2, 4, 9, 8, 17, 18, 16, 33, 34, 36, 32, 65, 66, 68, 72, 64, 129, 130, 132, 136, 144, 128, 257, 258, 260, 264, 272, 288, 256, 513, 514, 516, 520, 528, 544, 576, 512, 1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1024, 2049, 2050, 2052, 2056, 2064, 2080, 2112

Offset: 1

Author

Leroy Quet, Jun 14 2007

Keywords

• nonn
• tabl

Examples

			Binary representations of the terms in the first few rows:
10
100, 1001
1000, 10001, 10010
10000, 100001, 100010, 100100
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A081118, A131095.

Programs

Haskell

import Data.List (sort, nub)
a131094 n k = a131094_tabl !! (n-1) !! (k-1)
a131094_row n = a131094_tabl !! (n-1)
a131094_tabl = [2] : f 2 [2] where
   f v ws = ys : f (v + 1) ys where
            ys = take v $ nub $ sort $ concatMap h ws
   h z = [2 * z, 4 * z + 1, 4 * z' + b] where (z', b) = divMod z 2
-- Reinhard Zumkeller, Feb 11 2015

Maple

A080791 := proc(n) local bdigs ; bdigs := convert(n,base,2) ; nops(bdigs)-add(i,i=bdigs) ; end: A131094 := proc(n) local a,i; a := [] ; i := 2^n ; while nops(a) < n do while A080791(i) <> n do i := i+1 ; od: a := [op(a),i] ; i := i+1 ; od: RETURN(a) ; end: seq(op(A131094(n)),n=1..10) ; # R. J. Mathar, Oct 17 2007

Extensions

More terms from R. J. Mathar, Oct 17 2007