A204458 Odd numbers not divisible by 17.

1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141

Offset

1,2

Comments

For the general case of odd numbers not divisible by a prime see a comment on A204454. There the o.g.f.s and the formulas are given.

The numerator polynomial of the o.g.f. given below has coefficients 1,2,2,2,2,2,2,2,4,2,2,2,2,2,2,2,1. See the row no. 7 of the array A204456. The first nine numbers are the first differences of the sequence if one starts with a(0):=0. The remaining ones are obtained by mirroring around the central number 4.

Compare with A192861: certain numbers from here are missing there, like 35, 49, 53, 71, 89, 97, 99, .. and others are missing here like 51, 85, 119, ...

Numbers coprime to 34. The asymptotic density of this sequence is 8/17. - Amiram Eldar, Oct 20 2020

Links

Table of n, a(n) for n=1..67.

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

Formula

O.g.f.: x*(1 + x^16 + 2*x*(1+x^8)*(Sum_{k=0..6} x^k) + 4*x^8)/((1-x^16)*(1-x)). The denominator can be factored.

a(n) = 2*n-1 + 2*floor((n+7)/16) = 2*n+1 + 2*floor((n-9)/16), n>=1. Note that for n=0 this is -1, but for the o.g.f. with start x^0 one uses a(0)=0.

a(n) = a(n-1) + a(n-16) - a(n-17). - Wesley Ivan Hurt, Oct 20 2020

Mathematica

Select[Range[141], CoprimeQ[#, 34] &] (* Amiram Eldar, Oct 20 2020 *)

Crossrefs

Cf. A204454 (also for more crossrefs), A204457.

Sequence in context: A373512 A294923 A005842 * A192861 A333854 A192868

Adjacent sequences: A204455 A204456 A204457 * A204459 A204460 A204461

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 07 2012

Status

approved