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A165413 a(n) is the number of distinct lengths of runs in the binary representation of n. 30
1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 1, 3, 2, 3, 2, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Least k whose value is n: 1, 4, 35, 536, 16775, 1060976, ..., = A165933. - Robert G. Wilson v, Sep 30 2009
LINKS
FORMULA
a(n) = 1 for n in A140690. - Robert G. Wilson v, Sep 30 2009
EXAMPLE
92 in binary is 1011100. There is a run of one 1, followed by a run of one 0, then a run of three 1's, then finally a run of two 0's. The run lengths are therefore (1,1,3,2). The distinct values of these run lengths are (1,3,2). Since there are 3 distinct values, then a(92) = 3.
MATHEMATICA
f[n_] := Length@ Union@ Map[ Length, Split@ IntegerDigits[n, 2]]; Array[f, 105] (* Robert G. Wilson v, Sep 30 2009 *)
PROG
(Haskell)
import Data.List (group, nub)
a165413 = length . nub . map length . group . a030308_row
-- Reinhard Zumkeller, Mar 02 2013
(PARI)
binruns(n) = {
if (n == 0, return([1, 0]));
my(bag = List(), v=0);
while(n != 0,
v = valuation(n, 2); listput(bag, v); n >>= v; n++;
v = valuation(n, 2); listput(bag, v); n >>= v; n--);
return(Vec(bag));
};
a(n) = #Set(select(k->k, binruns(n)));
vector(105, i, a(i)) \\ Gheorghe Coserea, Sep 17 2015
(Python)
from itertools import groupby
def a(n): return len(set([len(list(g)) for k, g in groupby(bin(n)[2:])]))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jan 04 2021
CROSSREFS
Cf. A140690 (locations of 1's), A165933 (locations of new highs).
Sequence in context: A022921 A080763 A245920 * A172155 A080573 A186440
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Sep 17 2009
EXTENSIONS
More terms from Robert G. Wilson v, Sep 30 2009
STATUS
approved

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)