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A204458 Odd numbers not divisible by 17. 5

%I

%S 1,3,5,7,9,11,13,15,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,

%T 53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,87,89,91,93,95,97,99,

%U 101,103,105,107,109,111,113,115,117,121,123,125,127,129,131,133,135,137,139,141

%N Odd numbers not divisible by 17.

%C 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.

%C 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.

%C 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, ...

%C Numbers coprime to 34. The asymptotic density of this sequence is 8/17. - _Amiram Eldar_, Oct 20 2020

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

%F 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.

%F 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.

%F a(n) = a(n-1) + a(n-16) - a(n-17). - _Wesley Ivan Hurt_, Oct 20 2020

%t Select[Range[141], CoprimeQ[#, 34] &] (* _Amiram Eldar_, Oct 20 2020 *)

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

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Feb 07 2012

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Last modified September 18 01:28 EDT 2021. Contains 347504 sequences. (Running on oeis4.)