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A035928
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Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order.
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11
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2, 10, 12, 38, 42, 52, 56, 142, 150, 170, 178, 204, 212, 232, 240, 542, 558, 598, 614, 666, 682, 722, 738, 796, 812, 852, 868, 920, 936, 976, 992, 2110, 2142, 2222, 2254, 2358, 2390, 2470, 2502, 2618, 2650, 2730, 2762, 2866, 2898, 2978, 3010, 3132, 3164
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers n such that A036044(n) = n.
Also: numbers such that n+BR(n) is in A000225={2^k-1} (with BR = binary reversed). - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 17 2007
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| If offset were 0, a(2n+1) - a(2n) = 2^[log2(n)+1].
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EXAMPLE
| 38 is such a number because 38=100110; complement to get 011001, then reverse bit order to get 100110.
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MAPLE
| [seq(ReflectBinSeq(j, (floor_log_2(j)+1)), j=1..256)];
ReflectBinSeq := (x, n) -> (((2^n)*x)+binrevcompl(x));
binrevcompl := proc(nn) local n, z; n := nn; z := 0; while(n <> 0) do z := 2*z + ((n+1) mod 2); n := floor(n/2); od; RETURN(z); end;
floor_log_2 := proc(n) local nn, i: nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi: nn := floor(nn/2); od: end; # Computes essentially the same as floor(log[2](n))
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PROG
| (PARI) for(n=1, 1000, l=length(binary(n)); b=binary(n); if(sum(i=1, l, abs(component(b, i)-component(b, l+1-i)))==l, print1(n, ", ")))
(PARI) for(i=0, 999, if(Set(vecextract(t=binary(i), "-1..1")+t)==["1"], print1(i", "))) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 17 2007
(Haskell)
a035928 n = a035928_list !! (n-1)
a035928_list = filter (\x -> a036044 x == x) [0, 2..]
-- Reinhard Zumkeller, Sep 16 2011
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CROSSREFS
| Cf. A061855.
Cf. A000225.
Intersection of A195064 and A195066; cf. A195063, A195065.
Sequence in context: A176978 A186630 A154391 * A014486 A166751 A071162
Adjacent sequences: A035925 A035926 A035927 * A035929 A035930 A035931
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KEYWORD
| nonn,nice,easy,base
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AUTHOR
| Mike Keith (domnei(AT)aol.com)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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