A322463 Reverse runs of zeros in binary expansion of n and convert back to decimal.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 19, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 40, 35, 36, 41, 44, 39, 34, 37, 42, 43, 38, 45, 46, 47, 48, 49, 52, 51, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 80, 67

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))

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

A000120(a(n)) = A000120(n).

A005811(a(n)) = A005811(n).

a(A164710(n)) = A164710(n).

a(A322464(n)) = A322464(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 zeros: "00", "0" and "0",
- we exchange the first and the third run, and the second remains in place,
- we obtain: "10101100",
- hence a(150) = 172.

Mathematica

a[n_] := Module[{s=Split[IntegerDigits[n, 2]]}, m=Length[s]; m2=m-Mod[m, 2]; If[m2>0, ind=Riffle[Range[1, m, 2], Range[m2, 1, -2]]; FromDigits[Flatten[s[[ind]]], 2], n]]; Array[a, 100, 0] (* Amiram Eldar, Dec 12 2018 *)

Prog

(PARI) a(n) = {
    my (r=n, z=[], v=0, p=1, i=0);
    while (r, my (l=valuation(r+(r%2), 2)); if (r%2==0, z=concat(l, z)); r\=2^l);
    while (n, my (l=valuation(n+(n%2), 2)); if (n%2, v+=(2^l-1)*p; p*=2^l, p*=2^z[i++]); n\=2^l);
    return (v);
}

Crossrefs

See A322464 for the variant where we reverse the runs of ones.

See A056539 for a similar sequence.

Cf. A000120, A005811, A164710.

Sequence in context: A247752 A291149 A363748 * A275156 A188459 A146295

Adjacent sequences: A322460 A322461 A322462 * A322464 A322465 A322466

Keyword

nonn,base,look

Author

Rémy Sigrist, Dec 09 2018

Status

approved