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%I #50 Nov 03 2022 05:44:16
%S 5,25,35,55,65,85,95,115,125,145,155,175,185,205,215,235,245,265,275,
%T 295,305,325,335,355,365,385,395,415,425,445,455,475,485,505,515,535,
%U 545,565,575,595,605,625,635,655,665,685,695,715,725,745,755,775,785
%N Multiples of 5 whose GCD with 6 is 1.
%C Third row of A083140.
%C Positions of 5 in A020639. - _Zak Seidov_, Apr 29 2015
%H Amiram Eldar, <a href="/A084967/b084967.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F Numbers of the form 5k for which gcd(5k, 6) = 1.
%F a(n) = 5*A007310(n). - _Adriano Caroli_, Oct 03 2010
%F From _Colin Barker_, Feb 24 2013: (Start)
%F a(n) = 5*(-3 + (-1)^n + 6*n)/2.
%F a(n) = a(n-1) + a(n-2) - a(n-3).
%F G.f.: 5*x*(x^2+4*x+1) / ((x-1)^2*(x+1)). (End)
%F Limit_{n->infinity} a(n)/n = A038111(3)/A038110(3) = 15. - _Vladimir Shevelev_, Jan 20 2015
%F For n > 2, a(n) = a(n-2) + 30. - _Zak Seidov_, Apr 29 2015
%F a(n) = A007310(A273669(n)). - _Antti Karttunen_, May 20 2017
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(10*sqrt(3)). - _Amiram Eldar_, Nov 03 2022
%t 5Select[ Range[160], GCD[ #, 2*3] == 1 & ]
%t Select[Range[5, 785, 10], Mod[#, 3] > 0 &] (* _Zak Seidov_, Apr 29 2015 *)
%t a[1] = 5; a[n_] := a[n] = a[n - 1] + 10*(2 - Mod[n, 2]); Table[a[n], {n, 50}] (* _Zak Seidov_, Apr 29 2015 *)
%o (PARI) is(n)=n%5==0 && gcd(n,6)==1 \\ _Charles R Greathouse IV_, Nov 19 2014
%o (PARI) list(lim)=5*select(k->gcd(n,6)==1, [1..lim\5]) \\ _Charles R Greathouse IV_, Nov 19 2014
%Y Cf. A038110, A038111, A083140, A063149, A007310 (5-rough numbers), A273669.
%Y Cf. A020639. - _Zak Seidov_, Apr 29 2015
%K nonn,easy
%O 1,1
%A _Robert G. Wilson v_, Jun 15 2003
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