A065502 Positive numbers divisible by 2 or 5; 1/n not purely periodic after decimal point.

2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 34, 35, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 94, 95, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114

Offset: 1

Author

Len Smiley, Nov 25 2001

Keywords

• nonn
• easy

Comments

Complement of A045572. - Reinhard Zumkeller, Nov 15 2009

Numbers that cannot be prefixed by a single digit to form a prime in decimal representation: A124665 is a subsequence. - Reinhard Zumkeller, Oct 22 2011

Up to 198, this is almost identical to "a(n) = n such that 3^n-1 is not squarefree", with the only exceptions being 39 and 117, which are not in this sequence. Why is that? - Felix Fröhlich, Oct 19 2014

The asymptotic density of this sequence is 3/5. - Amiram Eldar, Mar 09 2021

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Crossrefs

Cf. A000035, A001622, A045572, A051628, A079998, A124665, A047229 (numbers divisible by 2 or 3).

Programs

Haskell

a065502 n = a065502_list !! (n-1)
a065502_list = filter ((> 1) . (gcd 10)) [1..]
-- Reinhard Zumkeller, Oct 22 2011

Maple

A065502 := proc(n)
     option remember;
     if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if (a mod 2) =0 or (a mod 5) =0 then
                return a;
            end if;
        end do:
    end if;
end proc; # R. J. Mathar, Jul 20 2012

Mathematica

Select[Range[114], Mod[#, 2] == 0 || Mod[#, 5] == 0 &] (* T. D. Noe, Jul 13 2012 *)
Select[ Range@ 114, MemberQ[{0, 2, 4, 5, 6, 8}, Mod[#, 10]] &] (* Robert G. Wilson v, May 22 2014 *)

PARI

isok(m) = ! ((m%2) && (m%5)); \\ Michel Marcus, Mar 09 2021

Formula

A000035(a(n))*(1-A079998(a(n)))=0. - Reinhard Zumkeller, Nov 15 2009

G.f.: x*(2*x^4+x^2+2) / ((x-1)^2*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Jul 18 2013

a(n) = 10*floor(n/6)+s(n mod 6)-floor(((n-1)mod 6)/5), where s(n) = n+1+floor((n+1)/3). - Gary Detlefs, Oct 05 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/5 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 28 2021

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 20 2009