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Search: id:A138103
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| A138103 |
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Numbers with an odd number of 1's in base 6 expansion. |
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+0
2
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| 1, 6, 8, 9, 10, 11, 13, 19, 25, 31, 36, 38, 39, 40, 41, 43, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 78, 80, 81, 82, 83, 85, 91, 97, 103, 109, 114, 116, 117, 118, 119, 121, 127, 133, 139, 145, 150, 152, 153, 154, 155, 157, 163
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is to A007092 (numbers in base 6) as A000069 (odious numbers: odd number of 1's in binary expansion) is to A007088 (numbers written in base 2) and as A137469 is to A007091 (numbers in base 5). Note that odd number of 1's in base 3 expansion is simply the odd numbers. This sequence includes, as a subset, A043373 = numbers n such that number of 1's in base 6 is 1.
This is strictly different from A043373.
Terms in this sequence but not in A043374 are 43, 223, 253, 258, 260, 261, 262, 263, 265, 271, 277, 283, 295,... - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008
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EXAMPLE
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a(1) = 1 because 1 base 10 = 1 base 6, which has an odd number (1) of ones.
a(2) = 6 because 6 base 10 = 10 base 6, which has an odd number (1) of ones.
a(3) = 8 because 8 base 10 = 12 base 6, which has an odd number (1) of ones.
a(11) = 36 because 36 base 10 = 100 base 6, which has an odd number (1) of ones.
a(17) = 43 because 43 base 10 = 111 base 6, which has an odd number (3) of ones.
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MAPLE
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isA138103 := proc(n) local a; a := 0 ; for d in convert(n, base, 6) do if d = 1 then a := a+1 ; fi ; od: RETURN( a mod 2 = 1) ; end: for n from 1 to 300 do if isA138103(n) then printf("%d, ", n) ; fi ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008
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CROSSREFS
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Cf. A000069, A007088, A007092, A043373, A137469.
Sequence in context: A043610 A043695 A076517 this_sequence A043373 A054047 A056653
Adjacent sequences: A138100 A138101 A138102 this_sequence A138104 A138105 A138106
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KEYWORD
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base,easy,nonn,less
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 03 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008
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