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

1,1

Comments

This is the complement of sequence A175381.

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A175381.

Sequence in context: A184108 A254760 A279289 * A279244 A325797 A128163

Adjacent sequences: A175379 A175380 A175381 * A175383 A175384 A175385

Keyword

base,nonn

Author

Leroy Quet, Apr 24 2010

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

Status

approved