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A037016
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Numbers n with property that reading binary expansion from right to left (least significant to most significant), run lengths do not decrease.
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8
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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, 58, 60, 61, 62, 63, 85, 101, 102, 106, 113, 114, 115, 117, 120, 121, 122, 124, 125, 126, 127, 170, 202, 204, 205, 213, 226, 227, 229, 230, 234, 240, 241, 242, 243, 245, 248
(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 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
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
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
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LINKS
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MATHEMATICA
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Select[ Range[0, 250], OrderedQ[ Reverse[ Length /@ Split[ IntegerDigits[#, 2] ] ] ]&] (* Jean-François Alcover, Apr 05 2013 *)
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PROG
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(Haskell)
import Data.List (unfoldr, group)
a037016 n = a037016_list !! (n-1)
a037016_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)
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CROSSREFS
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KEYWORD
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nonn,easy,base,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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