A164564 A positive integer n is included if there are at least two distinct odd numerical values of substrings in the binary representation of n that are not coprime to each other.

15, 19, 25, 27, 30, 31, 38, 39, 43, 45, 47, 50, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 67, 71, 75, 76, 77, 78, 79, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123

Offset

1,1

Links

Table of n, a(n) for n=1..62.

Example

27 in binary is 11011. The substrings of this, each with a distinct odd numerical value, (and their decimal equivalents) are 1 (1), 11 (3), 101 (5), 1011 (11), 1101 (13), 11011 (27). Since 3 is not coprime to 27, then 27 is in this sequence.
However, 21 in binary is 10101. The distinct odd substrings are 1, 101 (5), and 10101 (21). Since 1, 5, and 21 are all coprime to each other, then 21 is not in this sequence.

Mathematica

S={}; Do[id=IntegerDigits[n, 2]; Le=Length@id;
FL=Flatten[Table[Partition[id, k, 1], {k, 2, Le}], 1];
fd=Select[Union[FromDigits[ #, 2]&/@FL], OddQ];
su=Subsets[fd, {2}]; If[Max[GCD@@#&/@su]>1, AppendTo[S, n]], {n, 200}]; S (* Zak Seidov, Aug 17 2009 *)

Crossrefs

Complement of A164563.

Sequence in context: A368827 A257020 A234849 * A211329 A104298 A032475

Adjacent sequences: A164561 A164562 A164563 * A164565 A164566 A164567

Keyword

base,nonn

Author

Leroy Quet, Aug 16 2009

Extensions

More terms from Zak Seidov, Aug 17 2009

Spelling corrected by Jason G. Wurtzel, Sep 04 2010

Status

approved