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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.

%I A131094 #13 Aug 24 2015 02:38:45
%S A131094 2,4,9,8,17,18,16,33,34,36,32,65,66,68,72,64,129,130,132,136,144,128,
%T A131094 257,258,260,264,272,288,256,513,514,516,520,528,544,576,512,1025,
%U A131094 1026,1028,1032,1040,1056,1088,1152,1024,2049,2050,2052,2056,2064,2080,2112
%N 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.
%H A131094 Reinhard Zumkeller, <a href="/A131094/b131094.txt">Rows n = 1..125 of triangle, flattened</a>
%e A131094 Binary representations of the terms in the first few rows:
%e A131094 10
%e A131094 100, 1001
%e A131094 1000, 10001, 10010
%e A131094 10000, 100001, 100010, 100100
%p A131094 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
%o A131094 (Haskell)
%o A131094 import Data.List (sort, nub)
%o A131094 a131094 n k = a131094_tabl !! (n-1) !! (k-1)
%o A131094 a131094_row n = a131094_tabl !! (n-1)
%o A131094 a131094_tabl = [2] : f 2 [2] where
%o A131094    f v ws = ys : f (v + 1) ys where
%o A131094             ys = take v $ nub $ sort $ concatMap h ws
%o A131094    h z = [2 * z, 4 * z + 1, 4 * z' + b] where (z', b) = divMod z 2
%o A131094 -- _Reinhard Zumkeller_, Feb 11 2015
%Y A131094 Cf. A081118, A131095.
%K A131094 nonn,tabl
%O A131094 1,1
%A A131094 _Leroy Quet_, Jun 14 2007
%E A131094 More terms from _R. J. Mathar_, Oct 17 2007