A236204 Numbers not divisible by 2, 3 or 11.

1, 5, 7, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 125, 127, 131, 133, 137, 139, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 175, 179, 181, 185, 191, 193, 197, 199, 203, 205

Offset: 1

Author

Oleg P. Kirillov, Jan 20 2014

Keywords

• nonn
• easy

Comments

All primes except 2, 3 and 11 are in this sequence. Any product of terms is also a term in the sequence. - Alonso del Arte, Feb 04 2014

Also integers n such that least prime factor of 32^n-1 is 31. - Giovanni Resta, Mar 22 2014

Numbers coprime to 66. The asymptotic density of this sequence is 10/33. - 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. A235583.

Programs

Mathematica

Select[2Range[125] - 1, GCD[#, 66] == 1 &] (* Alonso del Arte, Feb 04 2014 *)

PARI

is(n)=gcd(n,66)==1 \\ Charles R Greathouse IV, Mar 26 2014

Formula

a(n) = a(n-1) + a(n-20) - a(n-21). - Charles R Greathouse IV, Mar 26 2014

For n > 20, a(n) = a(n - 20) + 66. - Zak Seidov, Mar 27 2014

G.f.: x*(x^20 + 4*x^19 + 2*x^18 + 6*x^17 + 4*x^16 + 2*x^15 + 4*x^14 + 2*x^13 + 4*x^12 + 2*x^11 + 4*x^10 + 2*x^9 + 4*x^8 + 2*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + 6*x^3 + 2*x^2 + 4*x + 1)/(x^21 - x^20 - x + 1). - Chai Wah Wu, Aug 03 2020