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 A175021 A positive integer n is included if n is not the smallest positive integer with its particular multiset of run-lengths (of either 0 or 1 considered together) in its binary representation. 2

%I #10 Sep 03 2017 21:30:35

%S 6,11,13,14,20,22,23,25,26,27,28,29,30,38,39,40,41,43,44,45,46,47,49,

%T 50,52,53,54,55,57,58,59,60,61,62,70,72,75,77,78,79,80,81,82,83,84,86,

%U 87,88,89,90,91,92,93,94,95,97,98,100,101,102,103,104,105,106,107,108,109

%N A positive integer n is included if n is not the smallest positive integer with its particular multiset of run-lengths (of either 0 or 1 considered together) in its binary representation.

%C A175020 contains those positive integers not in this sequence.

%H Michael De Vlieger, <a href="/A175021/b175021.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 in binary is 1001. The run lengths form the multiset (1,2,1). Since no positive integer < 9 has this same multiset of run lengths, then 9 is not in this sequence. On the other hand, 23 in binary is 10111. The run-lengths are (1,1,3). But 17 (which is < 23) in binary is 10001, which has the run-lengths of (1,3,1). Since the multisets (1,1,3) and (1,3,1) are identical, then 23 is in this sequence.

%t Block[{nn = 109, s}, s = Array[Sort@ Map[Length, Split@ IntegerDigits[#, 2]] &, nn]; Complement[Range[nn], Values[PositionIndex@ s][[All, 1]] ]] (* _Michael De Vlieger_, Sep 03 2017 *)

%Y Cf. A175020.

%K base,nonn

%O 1,1

%A _Leroy Quet_, Nov 03 2009

%E Extended by _Ray Chandler_, Mar 11 2010

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)