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 A043569 Numbers whose base-2 representation has exactly 2 runs. 8
 2, 4, 6, 8, 12, 14, 16, 24, 28, 30, 32, 48, 56, 60, 62, 64, 96, 112, 120, 124, 126, 128, 192, 224, 240, 248, 252, 254, 256, 384, 448, 480, 496, 504, 508, 510, 512, 768, 896, 960, 992, 1008, 1016, 1020, 1022, 1024, 1536, 1792, 1920, 1984, 2016, 2032, 2040, 2044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Mersenne numbers (A000225) times powers of 2 (A000079). Therefore this sequence contains the even perfect numbers (A000396). - Alonso del Arte, Apr 21 2006 LINKS Lei Zhou, Table of n, a(n) for n = 1..10000 FORMULA This sequence is twice A023758. - Franklin T. Adams-Watters, Apr 21 2006 Sum_{n>=1} 1/a(n) = A065442. - Amiram Eldar, Feb 20 2022 MAPLE 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 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 MATHEMATICA Take[Sort[Flatten[Table[(2^x - 1)*(2^y), {x, 32}, {y, 32}]]], 54] (* Alonso del Arte, Apr 21 2006 *) PROG (Python) def ok(n): b = bin(n)[2:]; return "10" in b and "01" not in b print([m for m in range(2045) if ok(m)]) # Michael S. Branicky, Feb 04 2021 (Python) def a_next(a_n): t = a_n >> 1; return (a_n | t) + (t & 1) a_n = 2; a = [] for i in range(54): a.append(a_n); a_n = a_next(a_n) # Falk Hüffner, Feb 19 2022 CROSSREFS Cf. A062289, A065442, A101082. Sequence in context: A043748 A043756 A043765 * A273131 A249721 A010063 Adjacent sequences:  A043566 A043567 A043568 * A043570 A043571 A043572 KEYWORD nonn,base AUTHOR EXTENSIONS More terms from Rick L. Shepherd, Nov 29 2004 STATUS approved

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Last modified June 26 20:13 EDT 2022. Contains 354885 sequences. (Running on oeis4.)