A192817 -id:A192817 - cp's OEIS frontend

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

Gary Detlefs, Oct 04 2013

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

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).

Cf. A007775, A192817.

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

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 *)

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

A201462 Numbers that are not coprime to their 9's complement.

Original entry on oeis.org

3, 6, 9, 11, 12, 15, 18, 21, 22, 24, 27, 30, 33, 36, 39, 42, 44, 45, 48, 51, 54, 55, 57, 60, 63, 66, 69, 72, 75, 77, 78, 81, 84, 87, 88, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 148, 150, 153, 156, 159

Offset: 1

Alonso del Arte, Dec 01 2011

All multiples of 3 are in this sequence. Multiples of 11 are in this sequence if they have an even number of digits or if they are also multiples of 3.

			22 is in the sequence because its 9's complement is 77 and gcd(22, 77) = 11 > 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A061601 (9's complement of n), A192817 (complement).

a201462 n = a201462_list !! (n-1)
a201462_list = [x | x <- [1..], gcd x (a061601 x) > 1]
-- Reinhard Zumkeller, Dec 03 2011

[n: n in [3..159] | Gcd(10^#Intseq(n)-1,n) gt 1]; // Bruno Berselli, Dec 02 2011

(* First run the program for A061601 to define nineComplement *) Select[Range[200], GCD[#, nineComplement[#]] > 1 &]

cp's OEIS Frontend

A229968 Numbers not divisible by 3 or 11.

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