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A037015
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Numbers n with property that, reading binary expansion of n from right to left, run lengths strictly increase.
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18
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0, 1, 3, 6, 7, 14, 15, 28, 30, 31, 57, 60, 62, 63, 120, 121, 124, 126, 127, 241, 248, 249, 252, 254, 255, 483, 496, 497, 504, 505, 508, 510, 511, 966, 993, 995, 1008, 1009, 1016, 1017, 1020, 1022, 1023, 1987, 1990, 2016, 2017, 2019, 2032, 2033, 2040, 2041, 2044
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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There are A000009(k) elements of this list consisting of k bits. - Jason Kimberley, Jan 22 2013
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for sequences related to binary expansion of n
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EXAMPLE
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From Jason Kimberley, Jan 30 2013: (Start)
Interleaved lines:
binary expansions,
corresponding run lengths (distinct partitions);
1,
1;
11,
2;
110, 111,
2,1; 3;
1110, 1111,
3,1; 4;
11100, 11110, 11111,
3,2; 4,1; 5;
111001, 111100, 111110, 111111,
3,2,1; 4,2; 5,1; 6;
1111000, 1111001, 1111100, 1111110, 1111111,
4,3; 4,2,1; 5,2; 6,1; 7;
11110001, 11111000, 11111001, 11111100, 11111110, 11111111
4,3,1; 5,3; 5,2,1; 6,2; 7,1; 8;
111100011, 111110000, 111110001, 111111000, 111111001, 111111100, 111111110, 111111111,
4,3,2; 5,4; 5,3,1; 6,3; 6,2,1; 7,2; 8,1; 9;
Notice the reversed sorting when a part corresponds to a run of 0's.
(End)
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MATHEMATICA
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Select[Range[0, 2500], Min[Differences[Length/@Split[ Reverse[ IntegerDigits[ #, 2]]]]]>0&] (* Harvey P. Dale, Nov 18 2014 *)
Select[Range[0, 2100], Max[Differences[Length/@Split[IntegerDigits[#, 2]]]]<0&] (* Harvey P. Dale, Jun 28 2020 *)
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PROG
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(Haskell)
import Data.List (group)
a037015 n = a037015_list !! (n-1)
a037015_list = filter (all (> 0) . ds) [0..] where
ds x = zipWith (-) (tail gs) gs where
gs = map length $ group $ a030308_row x
-- Reinhard Zumkeller, Jul 31 2013, Mar 10 2012
(Python)
from itertools import groupby
A037015_list = []
for n in range(10**5):
c = None
for x, y in groupby(bin(n)[2:]):
z = len(list(y))
if c != None and z >= c:
break
c = z
else:
A037015_list.append(n) # Chai Wah Wu, Sep 14 2021
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CROSSREFS
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Subsequence of A037016, cf. A037013, A037014.
Cf. A030308.
Sequence in context: A099403 A324726 A333379 * A138218 A056055 A070523
Adjacent sequences: A037012 A037013 A037014 * A037016 A037017 A037018
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KEYWORD
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nonn,easy,base,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Patrick De Geest, Feb 15 1999
Offset fixed and missing 1023 inserted by Reinhard Zumkeller, Mar 10 2012
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STATUS
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approved
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