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A051382
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Numbers n such that base 3 expansion matches (0|1)*(02)?(0|1)* (no more than one "02" allowed in midst of 0's and 1's).
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2
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1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 18, 19, 21, 22, 27, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 40, 54, 55, 57, 58, 63, 64, 66, 67, 81, 82, 83, 84, 85, 87, 88, 90, 91, 92, 93, 94, 99, 100, 102, 103, 108, 109, 110, 111, 112, 114, 115, 117, 118, 119, 120, 121, 162, 163
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Representation of 2n in base 3 consists entirely of 0's and 2's, except possibly for a single pair of adjacent 1's among them.
9 divides neither C(2s-1,s) (= A001700[ s ]) nor C(2s,s) (= A000984[ s ]) if and only if s=a(n)
Representation of 2n in base 3 consists entirely of 0's and 2's, except possibly for a pair of adjacent 1's
9 does not divide C(2s-1,s) (= A001700[ s ]) if and only if s=a(n)
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| In base 3 the terms look like 1, 2, 10, 11, 20, 21, 100, 101, 102, 110, 111, 200, 201, 210, 211, 1000, 1001, 1002, 1010, 1011, 1020, 1021, 1100, 1101, 1102, 1110, 1111, 2000, 2001, 2010, 2011, 2100, 2101, 2 110, 2111, 10000
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PROG
| (Perl) sub conv_x_base_n { my($x, $b) = @_; my ($r, $z) = (0, ''); do { $r = $x % $b; $x = ($x - $r)/$b; $z = "$r" . $z; } while(0 != $x); return($z); }
(Perl) for($i=1; $i <= 201; $i++) { if(("0" . conv_x_base_n($i, 3)) =~ /^(0|1)*(02)?(0|1)*$/) { print $i, ", "; } }
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CROSSREFS
| Cf. A046097, A048645, A037468, A005836.
Sequence in context: A065904 A039108 A020756 * A026514 A039054 A047519
Adjacent sequences: A051379 A051380 A051381 * A051383 A051384 A051385
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net), Antti Karttunen Oct 24 1999
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