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A065502
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Positive numbers divisible by 2 or 5; 1/n not purely periodic after decimal point.
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10
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(PARI) { n=0; for (m=1, 10^9, if (m%2 == 0 || m%5 == 0, write("b065502.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 20 2009
(PARI) isok(m) = ! ((m%2) && (m%5)); \\ Michel Marcus, Mar 09 2021
(Haskell)
a065502 n = a065502_list !! (n-1)
a065502_list = filter ((> 1) . (gcd 10)) [1..]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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