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%I #43 Oct 10 2019 03:55:32
%S 0,1,2,3,5,6,7,10,12,13,14,15,21,25,26,28,29,30,31,42,50,51,53,56,57,
%T 58,60,61,62,63,85,101,102,106,113,114,115,117,120,121,122,124,125,
%U 126,127,170,202,204,205,213,226,227,229,230,234,240,241,242,243,245,248
%N Numbers n with property that reading binary expansion from right to left (least significant to most significant), run lengths do not decrease.
%C There are A000041(k) elements of this list consisting of k bits: a partition of k written in nonincreasing order corresponds to the binary expansion which when read left to right has run lengths as listed in the partition (reading left to right forces the initial run to be of 1s). - _Jason Kimberley_, Feb 08 2013
%C This sequence is a subsequence of A061854 (if we allow the initial 0 to be represented by the empty bit string). - _Jason Kimberley_, Feb 08 2013
%C The positive entries are those n for which row n of A101211 is weakly decreasing. Example: 6 is in the sequence because row 6 of A101211 is [2,1]; 8 is not in the sequence because row 8 of A101211 is [1,3]. - _Emeric Deutsch_, Jan 21 2018
%H Reinhard Zumkeller, <a href="/A037016/b037016.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%t Select[ Range[0, 250], OrderedQ[ Reverse[ Length /@ Split[ IntegerDigits[#, 2] ] ] ]&] (* _Jean-François Alcover_, Apr 05 2013 *)
%o (Haskell)
%o import Data.List (unfoldr, group)
%o a037016 n = a037016_list !! (n-1)
%o a037016_list = 0 : filter
%o (all (>= 0) . (\x -> zipWith (-) (tail $ rls x) $ rls x)) [1..] where
%o rls = map length . group . unfoldr
%o (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
%o -- _Reinhard Zumkeller_, Mar 10 2012
%Y Cf. A037015 (subsequence), A037014, A037013.
%K nonn,easy,base,nice
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Patrick De Geest_, Feb 15 1999
%E Offset fixed by _Reinhard Zumkeller_, Mar 10 2012
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