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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 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 0's. (End) MATHEMATICA 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 *) 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 (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 CROSSREFS 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 KEYWORD nonn,easy,base,nice AUTHOR EXTENSIONS More terms from Patrick De Geest, Feb 15 1999 Offset fixed and missing 1023 inserted by Reinhard Zumkeller, Mar 10 2012 STATUS approved

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Last modified May 24 21:08 EDT 2022. Contains 354043 sequences. (Running on oeis4.)