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A071904
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Odd composite numbers.
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93
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9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 121, 123, 125, 129, 133, 135, 141, 143, 145, 147, 153, 155, 159, 161, 165, 169, 171, 175, 177, 183, 185, 187, 189, 195, 201, 203, 205
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listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Same as A014076 except for the initial term A014076(1)=1 (which is not a composite number).
Values of quadratic form (2x + 3)*(2y + 3) = 4xy + 6x + 6y + 9 for x, y >= 0. - Anton Joha, Jan 21 2001
Composite numbers n such that (n-1)^(n-1) == 1 (mod n). - Michel Lagneau, Feb 18 2012
There is a rectangular array of n dots (with both sides > 1) with a unique center point if and only if n is in this sequence. - Peter Woodward, Apr 21 2015
Let r(n) = (a(n)-1)/(a(n)+1)) if a(n) mod 4 = 1, (a(n)+1)/(a(n)-1)) otherwise; then Product_{n>=1} r(n) = (4/5) * (8/7) * (10/11) * (12/13) * (14/13) * ... = Pi/4. - Dimitris Valianatos, May 24 2017
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LINKS
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FORMULA
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EXAMPLE
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45 is in the sequence because it is odd and composite (45 = 3 * 3 * 5).
195 is in the sequence because it is odd and composite (195 = 3 * 5 * 13).
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MAPLE
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remove(isprime, [seq(2*i+1, i = 1 .. 1000)]); # Robert Israel, Apr 22 2015
# alternative
if n = 1 then
9;
else
for a from procname(n-1)+2 by 2 do
if not isprime(a) then
return a;
end if;
end do:
end if;
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MATHEMATICA
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With[{upto = 200}, Complement[Range[9, upto, 2], Prime[Range[ PrimePi[ upto]]]]] (* Harvey P. Dale, Jan 24 2013 *)
With[{upto = 200}, oddsequence=Table[2n+1, {n, 1, upto}]; oddcomposites=Union[Flatten[Range[oddsequence^2, upto, 2*oddsequence]]]] (* Ben Engelen, Feb 24 2016 *)
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PROG
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(Haskell)
a071904 n = a071904_list !! (n-1)
a071904_list = filter odd a002808_list
(PARI) lista(nn) = forcomposite(n=1, nn, if (n%2, print1(n, ", "))); \\ Michel Marcus, Sep 24 2016
(Python)
from sympy import isprime
def ok(n): return n > 3 and n%2 == 1 and not isprime(n)
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CROSSREFS
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KEYWORD
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nice,nonn,easy
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AUTHOR
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STATUS
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approved
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