A335835 Sort the run lengths in binary expansion of n in desccending order (with multiplicities).

0, 1, 2, 3, 6, 5, 6, 7, 14, 13, 10, 13, 12, 13, 14, 15, 30, 29, 26, 25, 26, 21, 26, 29, 28, 25, 26, 25, 28, 29, 30, 31, 62, 61, 58, 57, 50, 53, 50, 57, 58, 53, 42, 53, 50, 53, 58, 61, 60, 57, 50, 51, 50, 53, 50, 57, 56, 57, 58, 57, 60, 61, 62, 63, 126, 125

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 descending order: 3, 2, 1, 1,
- so the binary representation of a(72) is "1110010",
- and a(72) = 114.

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), , 4)) }

Crossrefs

Cf. A005811, A037016 (fixed points), A070939, A101211, A335834.

Sequence in context: A340774 A345068 A057723 * A361480 A142151 A003968

Adjacent sequences: A335832 A335833 A335834 * A335836 A335837 A335838

Keyword

nonn,base,look,easy

Author

Rémy Sigrist, Jun 26 2020

Status

approved