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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.
1
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
COMMENTS
This is a complement of sequence A164563.
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
Contribution from Zak Seidov, Aug 17 2009: (Start)
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 (End)
CROSSREFS
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