A160542 Not divisible by 11.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112

Offset: 1

Author

Zerinvary Lajos, May 18 2009

Keywords

• nonn
• easy

Comments

Contains numbers like 100, 111, 112, 113 which are not in A043096. - R. J. Mathar, May 20 2009

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A043096.

Programs

Maple

A160541 := proc(n)
    option remember ;
    if n <= 10 then
        n;
    else
        procname(n-10)+11 ;;
    end if;
end proc:
seq(A160541(n),n=1..100) ; # R. J. Mathar, Aug 05 2022

Mathematica

Select[Table[n,{n,200}],Mod[#,11]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{1,2,3,4,5,6,7,8,9,10,12},70] (* Harvey P. Dale, Sep 16 2020 *)

Sage

[i for i in range(72) if gcd(11, i) == 1]

Formula

a(n) = a(n-10) + 11, n>10. - R. J. Mathar, May 20 2009

G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10) / ( (1+x)*(1+x+x^2+x^3+x^4)*(x^4-x^3+x^2-x+1)*(x-1)^2 ). - R. J. Mathar, May 02 2014

Sum_{n>=1} (-1)^(n+1)/a(n) = (cot(Pi/11) - cot(2*Pi/11) + tan(Pi/22) - tan(3*Pi/22) + tan(5*Pi/22)) * Pi/11. - Amiram Eldar, May 11 2025