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

Author

Reinhard Zumkeller, Nov 30 2009

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

• 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).

Crossrefs

Complement of A008594.

Cf. A109015, A168185.

All three of A023805, A160453, A168186 are different.

Programs

Mathematica

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

Formula

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