A068780 Composite numbers n such that n+1 is also composite.

8, 9, 14, 15, 20, 21, 24, 25, 26, 27, 32, 33, 34, 35, 38, 39, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 62, 63, 64, 65, 68, 69, 74, 75, 76, 77, 80, 81, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 104, 105, 110, 111, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124

Offset

1,1

Comments

For all primes p, neither p nor p-1 is in the sequence. - Jon Perry, Oct 12 2014

Links

J. Stauduhar, Table of n, a(n) for n = 1..10000

Formula

There are x - 2x/log x + O(x/log^2 x) members up to x. The coefficient of the next asymptotic term depends on the quantitative version of the twin prime conjecture (though it can be bounded between -0.6796763684 and 2.4885722184, with the former conjectured to be the case). - Charles R Greathouse IV, Dec 19 2018

Maple

q:= n-> andmap(not isprime, [n, n+1]):
select(q, [$1..150])[];  # Alois P. Heinz, Jun 24 2021

Mathematica

Select[ Range[2, 200], !PrimeQ[ # ] && !PrimeQ[ # + 1] &]

Prog

(Magma) [n: n in [1..200] | not IsPrime(n) and not IsPrime(n+1)]; // Vincenzo Librandi, Oct 17 2014
(PARI) is(n)=!isprime(n) && !isprime(n+1) \\ Charles R Greathouse IV, Dec 19 2018

Crossrefs

Cf. A001359.

Equals A005381(n) - 1.

Sequence in context: A308893 A083134 A299143 * A174041 A096784 A175859

Adjacent sequences: A068777 A068778 A068779 * A068781 A068782 A068783

Keyword

nonn,easy

Author

Robert G. Wilson v, Mar 04 2002

Extensions

Definition reworded by N. J. A. Sloane, Aug 24 2012

Status

approved