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%I #12 Jan 31 2021 20:33:18
%S 1,2,3,8,5,42,7,8,9,10,11,672,13,14,15,32,17,522,19,40,21,682,23,672,
%T 25,130,27,56,29,2730,31,32,33,34,35,8352,37,190,195,40,41,42,43,2728,
%U 45,46,47,672,49,650,51,520,53,702,55,56,171,58,59,174720,61,62,189,128,195,8382,67,136,207,910,71,8352,73,3626,75
%N a(n) is the smallest positive multiple k of n such that every length of the runs of 0's and 1's in the binary representation of k is coprime to n.
%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 ends by either the digit 1-b or by the end of the string.
%e For n = 4, we check: 4 in binary is 100, which has a run of two 0's; and 2 is not coprime to 4. But 2*4 = 8 = 1000 in binary has a run of one 1 and a run of three 0's. Since both 1 and 3 are coprime to 4, a(4) = 8.
%Y Cf. A162535, A162536.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Jul 05 2009
%E More terms from _Sean A. Irvine_, Jan 27 2011
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