A229968 -id:A229968 - cp's OEIS frontend

A235933 Numbers coprime to 35.

1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 43, 44, 46, 47, 48, 51, 52, 53, 54, 57, 58, 59, 61, 62, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 78, 79, 81, 82, 83, 86, 87, 88, 89, 92, 93, 94, 96, 97, 99

Offset: 1

Oleg P. Kirillov, Jan 17 2014

The asymptotic density of this sequence is 24/35. - Amiram Eldar, Oct 23 2020

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

Cf. A160547 (numbers coprime to 31), A229968 (numbers coprime to 33), A204458 (numbers coprime to 34), A007310 (numbers coprime to 36).

Cf. A045572 (numbers not divisible by 5 or 2), A229829 (numbers not divisible by 5 or 3), A047201 (numbers not divisible by 5), A236207 (numbers not divisible by 5 or 11).

a235933 n = a235933_list !! (n-1)
a235933_list = filter ((== 1) . gcd 35) [1..]
-- Reinhard Zumkeller, Mar 27 2014

[n: n in [1..100] | GCD(n,35) eq 1]; // Bruno Berselli, Mar 27 2014

Select[Range[100], GCD[#, 35] == 1 &] (* Bruno Berselli, Mar 27 2014 *)

[i for i in range(100) if gcd(i, 35) == 1] # Bruno Berselli, Mar 27 2014

Signature corrected from Georg Fischer, Feb 07 2021

Erroneous recurrence removed from Bruno Berselli, Feb 08 2021

A229973 Numbers coprime to 39.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22, 23, 25, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 53, 55, 56, 58, 59, 61, 62, 64, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 92, 94, 95, 97, 98, 100, 101, 103, 106

Offset: 1

Gary Detlefs, Oct 04 2013

Numbers not divisible by 3 or 13.
For n from 1 to 24, a(n) mod 39-n - floor(11*n/25)-2*floor(n/8) has a period of 24, consisting of all zeros except a -2 at indices 8, 16, and 24.
The asymptotic density of this sequence is 8/13. - 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 (2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1).

Cf. A160545, A229829, A229968.

for n from 1 to 50 do if n mod 3<>0 and n mod 13<>0 then print(n) fi od

CoefficientList[Series[(x^22 + x^20 + x^18 + x^16 + 2 x^14 - x^12 + 3 x^11 - x^10 + 2 x^8 + x^6 + x^4 + x^2 + 1)/((x - 1)^2 (x + 1) (x^2 - x + 1) (x^2 + 1) (x^4 - x^2 + 1) (x^4 + 1) (x^8 - x^4 + 1)), {x, 0, 80}], x] (* Vincenzo Librandi, Oct 08 2013 *)
Select[Range[100], CoprimeQ[39, #] &] (* Amiram Eldar, Oct 23 2020 *)

a(n+24) = a(n) + 39.
a(n) = 39*floor((n-1)/24) + f(n) + floor(11*f(n)/25) + 2*floor(f(n)/8) - 2*floor(((n-1)mod 8)/7) + 40*floor(f(n-1)/23), where f(n) = n mod 24.
G.f.: x*(x^22+x^20+x^18+x^16+2*x^14-x^12+3*x^11-x^10+2*x^8+x^6+x^4+x^2+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)*(x^4+1)*(x^8-x^4+1)). - Colin Barker, Oct 07 2013

More terms from Colin Barker, Oct 07 2013

a(34) corrected by Vincenzo Librandi, Oct 08 2013

A236217 Numbers not divisible by 3, 5 or 11.

Original entry on oeis.org

1, 2, 4, 7, 8, 13, 14, 16, 17, 19, 23, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 46, 47, 49, 52, 53, 56, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 82, 83, 86, 89, 91, 92, 94, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118, 119, 122, 124, 127, 128

Offset: 1

Oleg P. Kirillov, Jan 20 2014

Numbers coprime to 165. The asymptotic density of this sequence is 16/33. - Amiram Eldar, Oct 23 2020

Bruno Berselli, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Intersection of: A160542 and A229829; A047201 and A229968; A001651, A047201 and A160542.

Cf. A236206, A236208.

Select[Range[200], Mod[#, 3] > 0 && Mod[#, 5] > 0 && Mod[#, 11] > 0 &] (* or *) Select[Range[200], Or @@ Divisible[#, {3, 5, 11}] == False &] (* Bruno Berselli, Mar 24 2014 *)
Select[Range[130], CoprimeQ[165, #] &] (* Amiram Eldar, Oct 23 2020 *)

a(n) = a(n-1) + a(n-80) - a(n-81) for n > 81. - Bruno Berselli, Mar 25 2014

A230193 Numbers divisible by 3 or 11.

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, 110, 111, 114, 117, 120, 121, 123, 126, 129, 132, 135, 138, 141, 143, 144, 147, 150, 153

Offset: 1

Gary Detlefs, Oct 11 2013

nonn

In general, sequences of numbers divisible by primes p and q have the form a(n+p+q-1) = a(n) + p*q.
Union of A008585 and A008593 (0 excluded). - Michel Marcus, Oct 16 2013
The asymptotic density of this sequence is 13/33. - Amiram Eldar, Mar 25 2021

Amiram Eldar, Table of n, a(n) for n = 1..10000

Complement of A229968.

Cf. A008585, A008593.

for n from 1 to 53 do if n mod 3 = 0 and n mod 11 = 0 then print(n) fi od

Select[Range[200], GCD[#, 33] > 1 &] (* T. D. Noe, Oct 15 2013 *)

a(n+13) = a(n) + 33.

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A235933 Numbers coprime to 35.

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A229973 Numbers coprime to 39.

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A236217 Numbers not divisible by 3, 5 or 11.

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A230193 Numbers divisible by 3 or 11.

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