A335834 Sort the run lengths in binary expansion of n in ascending order (with multiplicities).

0, 1, 2, 3, 4, 5, 4, 7, 8, 11, 10, 11, 12, 11, 8, 15, 16, 23, 20, 19, 20, 21, 20, 23, 24, 19, 20, 19, 24, 23, 16, 31, 32, 47, 40, 39, 44, 43, 44, 39, 40, 43, 42, 43, 44, 43, 40, 47, 48, 39, 44, 51, 44, 43, 44, 39, 56, 39, 40, 39, 48, 47, 32, 63, 64, 95, 80, 79

Offset

0,3

Comments

This sequence preserves the number of runs (A005811) and the length (A070939) of the binary representation of a number.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

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

Example

For n = 72:
- the binary representation of 72 is "1001000",
- the corresponding run lengths are: 1, 2, 1, 3,
- in ascending order: 1, 1, 2, 3,
- so the binary representation of a(72) is "1011000",
- and a(72) = 88.

Mathematica

Array[FromDigits[Flatten@ MapIndexed[ConstantArray[Mod[First[#2], 2], #1] &, Sort[Length /@ Split[IntegerDigits[#, 2]]]], 2] &, 67] (* Michael De Vlieger, Jun 27 2020 *)

Prog

(PARI) torl(n) = { my (rr=[]); while (n, my (r=valuation(n+(n%2), 2)); rr = concat(r, rr); n\=2^r); rr }
fromrl(rr) = { my (v=0); for (k=1, #rr, v = (v+(k%2))*2^rr[k]-(k%2)); v }
a(n) = { fromrl(vecsort(torl(n))) }

Crossrefs

Cf. A005811, A037014 (fixed points), A070939, A101211, A335835.

Sequence in context: A361479 A075054 A158366 * A289321 A301534 A373798

Adjacent sequences: A335831 A335832 A335833 * A335835 A335836 A335837

Keyword

nonn,base,look,easy

Author

Rémy Sigrist, Jun 26 2020

Status

approved