A037013 Reading binary expansion from right to left, run lengths strictly decrease.

0, 1, 3, 4, 7, 8, 15, 16, 24, 31, 32, 39, 48, 63, 64, 79, 96, 112, 127, 128, 143, 159, 192, 224, 255, 256, 287, 319, 384, 399, 448, 480, 511, 512, 543, 575, 624, 639, 768, 799, 896, 960, 1023, 1024, 1087, 1151, 1248, 1279, 1536, 1567, 1599, 1792, 1920, 1984, 2047, 2048, 2111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base
• nice

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to binary expansion of n

Crossrefs

Subsequence of A037014, cf. A037015, A037016.

Programs

Haskell

import Data.List (unfoldr, group)
a037013 n = a037013_list !! (n-1)
a037013_list = 0 : filter
   (all (< 0) . (\x -> zipWith (-) (tail $ rls x) $ rls x)) [1..] where
       rls = map length . group . unfoldr
             (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Mar 10 2012

Mathematica

Select[Range[0,2200],Min[Differences[Length/@Split[ IntegerDigits[ #,2]]]]>0&] (* Harvey P. Dale, Dec 17 2012 *)

Extensions

More terms from Patrick De Geest, Feb 15 1999

Offset fixed and missing 1024 and 2047 inserted by Reinhard Zumkeller, Mar 10 2012