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%I #13 Aug 24 2015 02:29:02
%S 2,4,9,17,18,20,33,34,36,40,65,66,68,72,80,129,130,132,136,144,160,
%T 257,258,260,264,272,288,320,513,514,516,520,528,544,576,640,1025,
%U 1026,1028,1032,1040,1056,1088,1152,1280,2049,2050,2052,2056,2064,2080,2112,2176
%N Triangle where n-th row contains the smallest n positive integers (listed in order) with exactly n nonleading 0's in their binary representations and where the smallest term in the n-th row is > that the largest term in the (n-1)th row.
%H Reinhard Zumkeller, <a href="/A131095/b131095.txt">Rows n = 1..125 of triangle, flattened</a>
%e Binary representations of the terms in the first few rows:
%e 10
%e 100, 1001
%e 10001, 10010, 10100
%e 100001, 100010, 100100, 101000
%p A023416 := proc(n) local brep,i ; brep := convert(n,base,2) ; add( 1-op(i,brep),i=1..nops(brep)) ; end: A131095 := proc(rowmax) local a,r,c ; a := 2 ; for r from 1 to rowmax do c := 1 ; while c <= r do if A023416(a) = r then printf("%d, ",a) ; c := c+1 ; fi ; a := a+1 ; od ; od ; end: A131095(10) ; # _R. J. Mathar_, Jun 15 2007
%o (Haskell)
%o import Data.List (sort, nub)
%o a131095 n k = a131095_tabl !! (n-1) !! (k-1)
%o a131095_row n = a131095_tabl !! (n-1)
%o a131095_tabl = [2] : [4, 9] : [17, 18, 20] : f 4 [17, 18, 20] where
%o f v ws = ys : f (v + 1) ys where
%o ys = take v $ dropWhile (<= last ws) $ nub $ sort $ concatMap h ws
%o h z = [2 * z, 4 * z + 1, 4 * z' + b] where (z', b) = divMod z 2
%o -- _Reinhard Zumkeller_, Feb 11 2015
%Y Cf. A081118, A131094.
%K nonn,tabl
%O 1,1
%A _Leroy Quet_, Jun 14 2007
%E More terms from _R. J. Mathar_, Jun 15 2007
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