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A043569 Numbers whose base-2 representation has exactly 2 runs. 8

%I

%S 2,4,6,8,12,14,16,24,28,30,32,48,56,60,62,64,96,112,120,124,126,128,

%T 192,224,240,248,252,254,256,384,448,480,496,504,508,510,512,768,896,

%U 960,992,1008,1016,1020,1022,1024,1536,1792,1920,1984,2016,2032,2040,2044

%N Numbers whose base-2 representation has exactly 2 runs.

%C Numbers whose binary representation contains the bit string "10" but not "01". Subsequence of A062289; set difference A062289 minus A101082. - _Rick L. Shepherd_, Nov 29 2004

%C Mersenne numbers (A000225) times powers of 2 (A000079). Therefore this sequence contains the even perfect numbers (A000396). - _Alonso del Arte_, Apr 21 2006

%H Lei Zhou, <a href="/A043569/b043569.txt">Table of n, a(n) for n = 1..10000</a>

%F This sequence is twice A023758. - _Franklin T. Adams-Watters_, Apr 21 2006

%p a:=proc(n) local nn,nd: nn:=convert(n,base,2): nd:={seq(nn[j]-nn[j-1],j=2..nops(nn))}: if n=2 then 2 elif nd={0,1} then n else fi end: seq(a(n),n=1..2100); # _Emeric Deutsch_, Apr 21 2006

%p a:=proc(n) local n2,d: n2:=convert(n,base,2): d:={seq(n2[j]-n2[j-1],j=2..nops(n2))}: if n=2 then 2 elif d={0,1} then n else fi end: seq(a(n),n=1..2100); # _Emeric Deutsch_, Apr 22 2006

%t Take[Sort[Flatten[Table[(2^x - 1)*(2^y), {x, 32}, {y, 32}]]], 54] (* _Alonso del Arte_, Apr 21 2006 *)

%o (Python)

%o def ok(n): b = bin(n)[2:]; return "10" in b and "01" not in b

%o print([m for m in range(2045) if ok(m)]) # _Michael S. Branicky_, Feb 04 2021

%Y Cf. A062289, A101082.

%K nonn,base

%O 1,1

%A _Clark Kimberling_

%E More terms from _Rick L. Shepherd_, Nov 29 2004

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Last modified June 14 20:21 EDT 2021. Contains 345038 sequences. (Running on oeis4.)