A084967 Multiples of 5 whose GCD with 6 is 1.

5, 25, 35, 55, 65, 85, 95, 115, 125, 145, 155, 175, 185, 205, 215, 235, 245, 265, 275, 295, 305, 325, 335, 355, 365, 385, 395, 415, 425, 445, 455, 475, 485, 505, 515, 535, 545, 565, 575, 595, 605, 625, 635, 655, 665, 685, 695, 715, 725, 745, 755, 775, 785

Offset: 1

Author

Robert G. Wilson v, Jun 15 2003

Keywords

• nonn
• easy
• changed

Comments

Third row of A083140.

Positions of 5 in A020639. - Zak Seidov, Apr 29 2015

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A038110, A038111, A083140, A007310 (5-rough numbers), A273669.

Cf. A020639. - Zak Seidov, Apr 29 2015

Essentially the same as A063149.

Programs

Mathematica

5Select[ Range[160], GCD[ #, 2*3] == 1 & ]
Select[Range[5, 785, 10], Mod[#, 3] > 0 &] (* Zak Seidov, Apr 29 2015 *)
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 *)

PARI

is(n)=n%5==0 && gcd(n,6)==1 \\ Charles R Greathouse IV, Nov 19 2014

PARI

list(lim)=5*select(k->gcd(n,6)==1, [1..lim\5]) \\ Charles R Greathouse IV, Nov 19 2014

Formula

Numbers of the form 5k for which gcd(5k, 6) = 1.

a(n) = 5*A007310(n). - Adriano Caroli, Oct 03 2010

From Colin Barker, Feb 24 2013: (Start)

a(n) = 5*(-3 + (-1)^n + 6*n)/2.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: 5*x*(x^2+4*x+1) / ((x-1)^2*(x+1)). (End)

Limit_{n->infinity} a(n)/n = A038111(3)/A038110(3) = 15. - Vladimir Shevelev, Jan 20 2015

For n > 2, a(n) = a(n-2) + 30. - Zak Seidov, Apr 29 2015

a(n) = A007310(A273669(n)). - Antti Karttunen, May 20 2017

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(10*sqrt(3)). - Amiram Eldar, Nov 03 2022