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 A035928 Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order. 27
 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, 3244 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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, Dec 17 2007 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith, Sums of Palindromes: an Approach via Nested-Word Automata, preprint arXiv:1706.10206 [cs.FL], June 30 2017. FORMULA If offset were 0, a(2n+1) - a(2n) = 2^floor(log_2(n)+1). EXAMPLE 38 is such a number because 38=100110; complement to get 011001, then reverse bit order to get 100110. 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)) # alternative Maple program: q:= n-> (l-> is(n=add((1-l[-i])*2^(i-1), i=1..nops(l))))(Bits[Split](n)): select(q, [\$1..3333])[];  # Alois P. Heinz, Feb 10 2021 MATHEMATICA bcrQ[n_]:=Module[{idn2=IntegerDigits[n, 2]}, Reverse[idn2/.{1->0, 0->1}] == idn2]; Select[Range[3200], bcrQ] (* Harvey P. Dale, May 24 2012 *) 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, Dec 17 2007 (PARI) a(n) = my (b=binary(n)); (n+1)*2^#b-fromdigits(Vecrev(b), 2)-1 \\ Rémy Sigrist, Mar 15 2021 (Haskell) a035928 n = a035928_list !! (n-1) a035928_list = filter (\x -> a036044 x == x) [0, 2..] -- Reinhard Zumkeller, Sep 16 2011 (Python) def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z}) def BCR(n): return int(comp(bin(n)[2:])[::-1], 2) def aupto(limit): return [m for m in range(limit+1) if BCR(m) == m] print(aupto(3244)) # Michael S. Branicky, Feb 10 2021 CROSSREFS Cf. A061855. Cf. A000225. Intersection of A195064 and A195066; cf. A195063, A195065. Sequence in context: A176978 A186630 A154391 * A014486 A166751 A216649 Adjacent sequences:  A035925 A035926 A035927 * A035929 A035930 A035931 KEYWORD nonn,nice,easy,base AUTHOR Mike Keith (domnei(AT)aol.com) EXTENSIONS More terms from Erich Friedman STATUS approved

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)