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A037015 Numbers n with property that, reading binary expansion of n from right to left, run lengths strictly increase. 18
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)
OFFSET

1,3

COMMENTS

There are A000009(k) elements of this list consisting of k bits. - Jason Kimberley, Jan 22 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences related to binary expansion of n

EXAMPLE

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 0s.

(End)

MATHEMATICA

Select[Range[0, 2500], Min[Differences[Length/@Split[ Reverse[ IntegerDigits[ #, 2]]]]]>0&] (* Harvey P. Dale, Nov 18 2014 *)

PROG

(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

CROSSREFS

Subsequence of A037016, cf. A037013, A037014.

Cf. A030308.

Sequence in context: A255683 A127307 A099403 * A138218 A056055 A070523

Adjacent sequences:  A037012 A037013 A037014 * A037016 A037017 A037018

KEYWORD

nonn,easy,base,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Patrick De Geest, Feb 1999

Offset fixed and missing 1023 inserted by Reinhard Zumkeller, Mar 10 2012

STATUS

approved

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Last modified January 20 12:50 EST 2019. Contains 319330 sequences. (Running on oeis4.)