A160453 -id:A160453 - cp's OEIS frontend

A168186 Positive numbers that are not multiples of 12.

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, 75, 76, 77, 78

Offset: 1

Reinhard Zumkeller, Nov 30 2009

121 (in decimal) is a member of this sequence but not a member of A023805. - Robert Munafo, Jan 26 2010

80 is a member of this sequence but is not a member of A160453. - Franklin T. Adams-Watters, Jan 26 2010

			156 is in A023805 but not in this sequence. - _Franklin T. Adams-Watters_, Jan 26 2010

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

Complement of A008594.
Cf. A109015, A168185.
All three of A023805, A160453, A168186 are different.

Select[Table[n,{n,200}],Mod[#,12]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011*)

A168185(a(n)) = 1.
A109015(a(n)) < 12.
From Chai Wah Wu, Jan 16 2020: (Start)
a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
G.f.: x*(x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^12 - x^11 - x + 1). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (12*sqrt(6) - 4*sqrt(3) + 6*sqrt(2) - 15)*Pi/72. - Amiram Eldar, May 12 2025

A023805 Xenodromes: all digits in base 11 are different.

Original entry on oeis.org

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

Olivier Gérard

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

			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

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

All three of A023805, A160453, A168186 are different.

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

cp's OEIS Frontend

A168186 Positive numbers that are not multiples of 12.

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