This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229829 #50 Sep 08 2022 08:46:06
%S A229829 1,2,4,7,8,11,13,14,16,17,19,22,23,26,28,29,31,32,34,37,38,41,43,44,
%T A229829 46,47,49,52,53,56,58,59,61,62,64,67,68,71,73,74,76,77,79,82,83,86,88,
%U A229829 89,91,92,94,97,98,101,103,104,106,107,109,112,113,116,118,119
%N A229829 Numbers coprime to 15.
%C A229829 A001651 INTERSECT A047201.
%C A229829 a(n) - 15*floor((n-1)/8) - 2*((n-1) mod 8) has period 8, repeating [1,0,0,1,0,1,1,0].
%C A229829 Numbers whose odd part is 7-rough: products of terms of A007775 and powers of 2 (terms of A000079). - _Peter Munn_, Aug 04 2020
%C A229829 The asymptotic density of this sequence is 8/15. - _Amiram Eldar_, Oct 18 2020
%H A229829 Amiram Eldar, <a href="/A229829/b229829.txt">Table of n, a(n) for n = 1..10000</a>
%H A229829 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F A229829 a(n+8) = a(n) + 15.
%F A229829 a(n) = 15*floor((n-1)/8) +2*f(n) +floor(2*phi*(f(n+1)+2)) -2*floor(phi*(f(n+1)+2)), where f(n) = (n-1) mod 8 and phi=(1+sqrt(5))/2.
%F A229829 a(n) = 15*floor((n-1)/8) +2*f(n) +floor((2*f(n)+5)/5) -floor((f(n)+2)/3), where f(n) = (n-1) mod 8.
%F A229829 From _Bruno Berselli_, Oct 01 2013: (Start)
%F A229829 G.f.: x*(1 +x +2*x^2 +3*x^3 +x^4 +3*x^5 +2*x^6 +x^7 +x^8) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)). -
%F A229829 a(n) = a(n-1) +a(n-8) -a(n-9) for n>9. (End)
%F A229829 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(7 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/15. - _Amiram Eldar_, Dec 13 2021
%p A229829 for n from 1 to 500 do if n mod 3<>0 and n mod 5<>0 then print(n) fi od
%t A229829 Select[Range[120], GCD[#, 15] == 1 &] (* or *) t = 70; CoefficientList[Series[(1 + x + 2 x^2 + 3 x^3 + x^4 + 3 x^5 + 2 x^6 + x^7 + x^8)/((1 - x)^2 (1 + x) (1 + x^2) (1 + x^4)) , {x, 0, t}], x] (* _Bruno Berselli_, Oct 01 2013 *)
%t A229829 Select[Range[120],CoprimeQ[#,15]&] (* _Harvey P. Dale_, Oct 31 2013 *)
%o A229829 (Magma) [n: n in [1..120] | IsOne(GCD(n,15))]; // _Bruno Berselli_, Oct 01 2013
%o A229829 (Sage) [i for i in range(120) if gcd(i, 15) == 1] # _Bruno Berselli_, Oct 01 2013
%Y A229829 Lists of numbers coprime to other semiprimes: A007310 (6), A045572 (10), A162699 (14), A160545 (21), A235933 (35).
%Y A229829 Cf. A008676, A078588, A113763, A160542, A160543, A160544.
%Y A229829 Subsequence of: A001651, A047201.
%Y A229829 Subsequences: A000079, A007775.
%K A229829 nonn,easy
%O A229829 1,2
%A A229829 _Gary Detlefs_, Oct 01 2013