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A128245 Smallest of three consecutive composite numbers whose sum is prime.

%I A128245 #15 Jul 24 2019 16:52:17
%S A128245 6,9,12,18,21,22,35,36,42,45,51,65,69,78,82,88,96,102,111,125,126,135,
%T A128245 138,161,162,165,166,172,189,198,209,232,249,255,256,261,275,291,292,
%U A128245 305,312,316,329,335,336,345,348,352,366,371,382,396,399,408,429,432
%N A128245 Smallest of three consecutive composite numbers whose sum is prime.
%C A128245 If n is a member of this sequence, either n+1 or n+2 is prime. This suggests that the density of the sequence is roughly kn/log^2 n for some k. Counts up to 10^9 suggest k is about 5.26. - _Charles R Greathouse IV_, Sep 11 2009
%H A128245 Harvey P. Dale, <a href="/A128245/b128245.txt">Table of n, a(n) for n = 1..1000</a>
%F A128245 By Rosser's theorem, a(2n) > n log n. - _Charles R Greathouse IV_, Sep 11 2009
%e A128245 6 + 8 + 9 = 23 = A060328(1);
%e A128245 9 + 10 + 12 = 31 = A060328(2);
%e A128245 12 + 14 + 15 = 41 = A060328(3);
%e A128245 18 + 20 + 21 = 59 = A060328(4).
%t A128245 CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; lst={};Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 15 2009 *)
%t A128245 Select[Partition[Select[Range[500],CompositeQ],3,1],PrimeQ[Total[#]]&][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 24 2019 *)
%o A128245 (PARI) test(n)={my(b=a+1,c);b+=isprime(b);c=b+1;c+=isprime(c);isprime(a+b+c)};for(n=4,1e3,if(!isprime(n)&&test(n),print1(n","))) \\ _Charles R Greathouse IV_, Sep 11 2009
%Y A128245 Cf. A060328.
%K A128245 nonn
%O A128245 1,1
%A A128245 _Zak Seidov_, May 03 2007