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.

5, 7, 9, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85

Offset: 1

Author

Leroy Quet, Apr 24 2010

Keywords

• base
• nonn

Comments

This is the complement of sequence A175381.

Includes all odd numbers > 3. - Robert Israel, Nov 25 2016

Examples

			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.
		

Links

• Jeremy Gardiner (up to n=226) and Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A175381.

Programs

Mathematica

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 *)

Extensions

Spelling corrected by Jason G. Wurtzel, Sep 04 2010

a(12)-a(56) from Lars Blomberg, May 05 2011

a(57)-a(66) from Nathaniel Johnston, May 05 2011