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A335834
Sort the run lengths in binary expansion of n in ascending order (with multiplicities).
3
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.
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
KEYWORD
nonn,base,look,easy
AUTHOR
Rémy Sigrist, Jun 26 2020
STATUS
approved