A037016 - OEIS

A037016

Numbers n with property that reading binary expansion from right to left (least significant to most significant), run lengths do not decrease.

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

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OFFSET

1,3

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

MATHEMATICA

Select[ Range[0, 250], OrderedQ[ Reverse[ Length /@ Split[ IntegerDigits[#, 2] ] ] ]&] (* Jean-François Alcover, Apr 05 2013 *)

PROG

(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