OFFSET
1,2
COMMENTS
Same as A071904 except for the initial term 1 (which is not composite).
Numbers n such that product of first n odd numbers divided by sum of the first n odd numbers is an integer : 1*3*5*...*(2*n - 1) / (1 + 3 + 5 + ... + (2*n - 1)) = c. - Ctibor O. Zizka, Jun 26 2010
Conjecture: There exist infinitely many pairs [a(n), a(n)+6] such that a(n)/3 and (a(n)+6)/3 are twin primes. - Eric Desbiaux, Sep 25 2014.
Odd numbers 2*n + 1 such that (2*n)!/(2*n + 1) is an integer. Odd terms of A056653. - Peter Bala, Jan 24 2017
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 2n. - Charles R Greathouse IV, Jul 02 2013
(a(n+2)-1)/2 - pi(a(n+2)-1) = n. - Anthony Browne, May 25 2016. Proof from Robert Israel: This follows by induction on n. If f(n) = (a(n+2)-1)/2 - pi(a(n+2)-1), one can show f(n+1) - f(n) = 1 (there are three cases to consider, depending on primeness of a(n+2) + 2 and a(n+2) + 4).
MAPLE
remove(isprime, [seq(i, i=1..1000, 2)]); # Robert Israel, May 25 2016
for n from 0 to 120 do
if irem(factorial(2*n), 2*n+1) = 0 then print(2*n+1) end if;
end do: # Peter Bala, Jan 24 2017
MATHEMATICA
Select[Range@210, !PrimeQ@ # && OddQ@ # &] (* Robert G. Wilson v, Sep 22 2008 *)
Select[Range[1, 199, 2], PrimeOmega[#] != 1 &] (* Alonso del Arte, Nov 19 2012 *)
PROG
(Haskell)
a014076 n = a014076_list !! (n-1)
a014076_list = filter ((== 0) . a010051) a005408_list
-- Reinhard Zumkeller, Sep 30 2011
(PARI) is(n)=n%2 && !isprime(n) \\ Charles R Greathouse IV, Nov 24 2012
(Python)
from sympy import primepi
def A014076(n):
if n == 1: return 1
m, k = n-1, primepi(n) + n - 1 + (n>>1)
while m != k:
m, k = k, primepi(k) + n - 1 + (k>>1)
return m # Chai Wah Wu, Jul 31 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved