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A162534 A positive integer k is included if every length of the runs of 0's and 1's in the binary representation of k divides k. 2

%I #20 Jan 31 2021 22:51:34

%S 1,2,4,5,6,10,12,16,18,20,21,22,24,26,36,38,42,44,48,50,52,54,60,65,

%T 69,72,74,76,78,80,81,82,84,85,86,87,90,93,95,100,102,106,108,114,117,

%U 120,125,126,130,132,138,144,146,148,150,154,156,160,162,164,166,168,170,172,174,176,178,180,182,186,188,190,192,198

%N A positive integer k is included if every length of the runs of 0's and 1's in the binary representation of k divides k.

%C By "run" of 0's or 1's, it is meant: Think of binary k as a string of 0's and 1's. A single run of the digit b (0 or 1) is made up completely of consecutive digits all equal to b, and is bounded on its end by either the digit 1-b or the end of the string.

%e 198 in binary is 11000110. There are two runs of two 1's each in this representation, and a run of three 0's and a run of one 0. Since 198 is divisible by each of these lengths (1,2, and 3), 198 is in the sequence.

%Y Cf. A162535, A162536.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jul 05 2009

%E More terms from _Sean A. Irvine_, Jan 26 2011

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