cp's OEIS Frontend

A175382 Positive integers n for which there is at least one positive integer k whose binary expansion occurs as a substring in the binary expansion of n but does not divide n.

%I A175382 #28 Nov 30 2016 05:43:19
%S A175382 5,7,9,11,13,14,15,17,18,19,21,22,23,25,26,27,28,29,30,31,33,34,35,37,
%T A175382 38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
%U A175382 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,81,82,83,84,85
%N A175382 Positive integers n for which there is at least one positive integer k whose binary expansion occurs as a substring in the binary expansion of n but does not divide n.
%C A175382 This is the complement of sequence A175381.
%C A175382 Includes all odd numbers > 3. - _Robert Israel_, Nov 25 2016
%H A175382 Jeremy Gardiner (up to n=226) and Ivan Neretin, <a href="/A175382/b175382.txt">Table of n, a(n) for n = 1..10000</a>
%e A175382 14 in binary is 1110. One of the substrings of 1110 is 11, which is 3 in decimal. Since 3 does not divide 14, 14 is in this sequence.
%t A175382 Select[Range@ 85, Function[n, Count[Map[IntegerDigits[#, 2] &, Complement[Range@ n, Divisors@ n]], k_ /; Length@ SequencePosition[IntegerDigits[n, 2], k] > 0] > 0]] (* _Michael De Vlieger_, Nov 24 2016, Version 10.1 *)
%Y A175382 Cf. A175381.
%K A175382 base,nonn
%O A175382 1,1
%A A175382 _Leroy Quet_, Apr 24 2010
%E A175382 Spelling corrected by _Jason G. Wurtzel_, Sep 04 2010
%E A175382 a(12)-a(56) from _Lars Blomberg_, May 05 2011
%E A175382 a(57)-a(66) from _Nathaniel Johnston_, May 05 2011