A138103 Numbers with an odd number of 1's in base 6 expansion.

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

Offset: 1

Author

Jonathan Vos Post, May 03 2008

Keywords

• base
• easy
• nonn
• less

Comments

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, May 13 2008

Examples

			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.
		

Links

• Index entries for 6-automatic sequences.

Crossrefs

Cf. A000069, A007088, A007092, A043373, A137469.

Programs

Maple

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, May 13 2008

Extensions

Corrected and extended by R. J. Mathar, May 13 2008