A023805 Xenodromes: all digits in base 11 are different.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base
• fini
• easy

Comments

Considering some base b, there are b numbers with 1 digit, (b-1)*(b-1) numbers with 2 digits -- since leading 0's are not allowed and the second digit must avoid the first. There are (b-1)*(b-1)*(b-2) numbers with 3 digits, (b-1)*(b-1)*(b-2)*..*(b-d+1) numbers with d digits, in total b+(b-1)*sum_{d=2..b} (b-1)!/(b-d)! = b+(b-1)^2* 2F0(1,2-b;;-1) = A001339(b-1). The formula is applicable to sequences A023798 - A023810. This sequence here as A001339(11-1) = 98641011 terms. [From R. J. Mathar, Jan 27 2010]

Last term is a(98641011) = 282458553905. - Charles R Greathouse IV, Jun 16 2012

Examples

			121 (in decimal) = 100 (base 11) is a member of A168186 but not a member of this sequence. - Robert Munafo, Jan 26 2010
156 is in A023805 but not in A168186. - Franklin T. Adams-Watters, Jan 26 2010
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

All three of A023805, A160453, A168186 are different.

Programs

Mathematica

Select[Range[0, 100], Max[DigitCount[#, 11]] == 1 &] (* Paolo Xausa, Mar 22 2025 *)