A229968 Numbers not divisible by 3 or 11.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 19, 20, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 46, 47, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106

Offset: 1

Author

Gary Detlefs, Oct 04 2013

Keywords

• nonn
• easy

Comments

Numbers coprime to 33.

For n from 1 to 20, a(n) mod 33 - n - floor(8*n/19) - 2*floor(n/7) has a period of 20 consisting of all zeros except for a -1 at index 7.

The first index where this differs from A192817 is n = 68; A192817(68) = 110 whereas a(68) = 112. - Tom Edgar, Feb 05 2015

The asymptotic density of this sequence is 20/33. - Amiram Eldar, Oct 23 2020

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A007775, A192817.

Programs

Maple

for n from 1 to 500 do if n mod 3<>0 and n mod 11 <>0 then print(n) fi od

Mathematica

Select[Range[132], GCD[#, 33] == 1 &] (* Alonso del Arte, Oct 05 2013 *)
Select[Range[200], Mod[#, 3]>0 && Mod[#, 11]>0 &] (* Vincenzo Librandi, Feb 08 2014 *)

Formula

a(n+20) = a(n) + 33.

a(n) = 33*floor((n-1)/20) + f(n) + floor(8*f(n)/19) + 2*floor(f(n)/7) - floor(f(n+12)/19) + 32*floor(f(n-1)/19), where f(n) = n mod 20.

a(n) = a(n-1)+a(n-20)-a(n-21). G.f.: x*(x^20 +x^19 +2*x^18 +x^17 +2*x^16 +x^15 +2*x^14 +3*x^13 +x^12 +2*x^11 +x^10 +2*x^9 +x^8 +3*x^7 +2*x^6 +x^5 +2*x^4 +x^3 +2*x^2 +x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)*(x^8 -x^6 +x^4 -x^2 +1)). - Colin Barker, Oct 08 2013