A068780 - OEIS

%I #26 Sep 08 2022 08:45:05

%S 8,9,14,15,20,21,24,25,26,27,32,33,34,35,38,39,44,45,48,49,50,51,54,

%T 55,56,57,62,63,64,65,68,69,74,75,76,77,80,81,84,85,86,87,90,91,92,93,

%U 94,95,98,99,104,105,110,111,114,115,116,117,118,119,120,121,122,123,124

%N Composite numbers n such that n+1 is also composite.

%C For all primes p, neither p nor p-1 is in the sequence. - _Jon Perry_, Oct 12 2014

%H J. Stauduhar, <a href="/A068780/b068780.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%p q:= n-> andmap(not isprime, [n, n+1]):

%p select(q, [$1..150])[];  # _Alois P. Heinz_, Jun 24 2021

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

%o (Magma) [n: n in [1..200] | not IsPrime(n) and not IsPrime(n+1)]; // _Vincenzo Librandi_, Oct 17 2014

%o (PARI) is(n)=!isprime(n) && !isprime(n+1) \\ _Charles R Greathouse IV_, Dec 19 2018

%Y Cf. A001359.

%Y Equals A005381(n) - 1.

%K nonn,easy

%O 1,1

%A _Robert G. Wilson v_, Mar 04 2002

%E Definition reworded by _N. J. A. Sloane_, Aug 24 2012