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A071904 Odd composite numbers. 93
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
Intersection of A002808 and A005408. - Reinhard Zumkeller, Oct 10 2011
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
First differences <= 6. Cf. A164510. - Zak Seidov, Sep 22 2016
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
LINKS
Zak Seidov and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov)
FORMULA
A000035(a(n))*(1-A010051(a(n))) = 1; A020639(a(n)) = A162022(n). - Reinhard Zumkeller, Oct 10 2011
a(n) ~ 2n. - Charles R Greathouse IV, Jul 02 2013
More precisely, a(n) = 2n(1 + 2(1+o(1))/log(n)). - Vladimir Shevelev, Jan 07 2015
EXAMPLE
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).
MAPLE
remove(isprime, [seq(2*i+1, i = 1 .. 1000)]); # Robert Israel, Apr 22 2015
# alternative
A071904 := proc(n) local a;
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;
end proc: # R. J. Mathar, Sep 09 2015
MATHEMATICA
Select[Table[n, {n, 9, 300, 2}], !PrimeQ[#] &] (* Vladimir Joseph Stephan Orlovsky, Apr 16 2011 *)
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 *)
PROG
(Haskell)
a071904 n = a071904_list !! (n-1)
a071904_list = filter odd a002808_list
-- Reinhard Zumkeller, Oct 10 2011
(PARI) is(n)=n%2 && !isprime(n) && n > 1 \\ Charles R Greathouse IV, Nov 24 2012
(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)
print(list(filter(ok, range(206)))) # Michael S. Branicky, Sep 15 2021
CROSSREFS
Cf. A164510.
Sequence in context: A160666 A039769 A270574 * A326586 A014076 A067800
KEYWORD
nice,nonn,easy
AUTHOR
Shyam Sunder Gupta, Jun 12 2002
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)