1,1

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

Every odd composite has at least two representations as a difference of two squares with opposite parity: the trivial difference of two consecutive squares and at least one other difference of two nonconsecutive squares. Odd primes and 1 have only the trivial difference. - Charles Kusniec, Aug 31 2025

K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov).

Joel E. Cohen and Dexter Senft, Gaps of size 2, 4, and (conditionally) 6 between successive odd composite numbers occur infinitely often, Notes on Number Theory and Discrete Mathematics, Volume 31, Number 3, 494-503 (2025). See p. 495.

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

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).

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

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 *)

(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

(Python)

from sympy import primepi

def A071904(n):

if n == 1: return 9

m, k = n, primepi(n) + n + (n>>1)

while m != k:

m, k = k, primepi(k) + n + (k>>1)

return m # Chai Wah Wu, Jul 31 2024

Cf. A002808, A014076, A005408, A000035, A010051, A020639, A162022.

Cf. A164510.

Sequence in context: A160666 A039769 A270574 * A326586 A014076 A067800

Adjacent sequences: A071901 A071902 A071903 * A071905 A071906 A071907

nice,nonn,easy

Shyam Sunder Gupta, Jun 12 2002

approved