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n written in fractional base 7/2.
2

%I #25 Jun 03 2019 02:02:02

%S 0,1,2,3,4,5,6,20,21,22,23,24,25,26,40,41,42,43,44,45,46,60,61,62,63,

%T 64,65,66,210,211,212,213,214,215,216,230,231,232,233,234,235,236,250,

%U 251,252,253,254,255,256,400,401,402,403,404,405,406,420,421,422,423,424,425

%N n written in fractional base 7/2.

%F To represent a number in base 7, if a digit exceeds 6, subtract 7 and carry 1. In the fractional base 7/2, subtract 7 and carry 2.

%e From _Alonso del Arte_, Apr 21 2019: (Start)

%e The integers 0 through 6 are written with the digits 0 through 6.

%e Then, since b = 7/2 is written as 10, and 7 is twice 7/2, 7 is 20 in base 7/2, and therefore a(7) = 20.

%e a(28) = 210 since 2 * (7/2)^2 + 1 * (7/2) = 2 * 49/4 + 1 * 7/2 = 98/4 + 14/4 = 112/4 = 28.

%e (End)

%t Select[Table[FromDigits[IntegerDigits[n, 7]], {n, 0, 230}], IntegerQ[FromDigits[IntegerDigits[#], 7/2]] &] (* _Alonso del Arte_, Apr 21 2019 *)

%Y Cf. A000079, A000420, A007093.

%K nonn,base

%O 0,3

%A _David W. Wilson_