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
Links
- J. Stauduhar, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n: n in [1..200] | not IsPrime(n) and not IsPrime(n+1)]; // Vincenzo Librandi, Oct 17 2014
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Maple
q:= n-> andmap(not isprime, [n, n+1]): select(q, [$1..150])[]; # Alois P. Heinz, Jun 24 2021
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Mathematica
Select[ Range[2, 200], !PrimeQ[ # ] && !PrimeQ[ # + 1] &] SequencePosition[Table[If[CompositeQ[n],1,0],{n,150}],{1,1}][[;;,1]] (* Harvey P. Dale, Feb 01 2025 *) -
PARI
is(n)=!isprime(n) && !isprime(n+1) \\ Charles R Greathouse IV, Dec 19 2018
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
Extensions
Definition reworded by N. J. A. Sloane, Aug 24 2012
Comments