A335835 Sort the run lengths in binary expansion of n in descending 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

Author

Rémy Sigrist, Jun 26 2020

Keywords

• nonn
• base
• look
• easy

Comments

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

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n

Crossrefs

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

Programs

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)) }

Formula

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