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 A322464 Reverse runs of ones in binary expansion of n and convert back to decimal. 2
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14, 15, 16, 17, 18, 25, 20, 21, 26, 29, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 34, 49, 36, 37, 50, 57, 40, 41, 42, 53, 52, 45, 58, 61, 48, 35, 38, 51, 44, 43, 54, 59, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 66, 97 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is a self-inverse permutation of nonnegative integers. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 0..2^18-1 (where the color is function of A005811(n)) FORMULA A000120(a(n)) = A000120(n). A005811(a(n)) = A005811(n). a(A322463(n)) = A322463(a(n)). a(2^n) = 2^n. a(2^n-1) = 2^n-1. EXAMPLE For n = 150: - the binary representation of 150 is "10010110", - we have three runs of ones: "1", "1" and "11", - we exchange the first and the third run, and the second remains in place, - we obtain: "11001010", - hence a(150) = 202. MATHEMATICA a[n_] := Module[{s=Split[IntegerDigits[n, 2]]}, m=Length[s]; If[m>1, m2 = m-1 + Mod[m, 2]; ind=Riffle[Range[m2, 1, -2], Range[2, m, 2]]; FromDigits[Flatten[ s[[ind]]], 2], n]]; Array[a, 120, 0] (* Amiram Eldar, Dec 12 2018 *) PROG (PARI) a(n) = {     my (r=n, o=[], v=0, p=1, i=0);     while (r, my (l=valuation(r+(r%2), 2)); if (r%2, o=concat(l, o)); r\=2^l);     while (n, my (l=valuation(n+(n%2), 2)); if (n%2, v+=(2^o[i++]-1)*p; p*=2^o[i], p*=2^l); n\=2^l);     return (v); } CROSSREFS See A322463 for the variant where we reverse the runs of zeros. Cf. A000120, A005811. Sequence in context: A108548 A333692 A333693 * A057889 A235027 A337304 Adjacent sequences:  A322461 A322462 A322463 * A322465 A322466 A322467 KEYWORD nonn,base,look AUTHOR Rémy Sigrist, Dec 09 2018 STATUS approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)