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

6, 9, 12, 18, 21, 22, 35, 36, 42, 45, 51, 65, 69, 78, 82, 88, 96, 102, 111, 125, 126, 135, 138, 161, 162, 165, 166, 172, 189, 198, 209, 232, 249, 255, 256, 261, 275, 291, 292, 305, 312, 316, 329, 335, 336, 345, 348, 352, 366, 371, 382, 396, 399, 408, 429, 432

Offset: 1

Author

Zak Seidov, May 03 2007

Keywords

• nonn

Comments

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

Examples

			6 + 8 + 9 = 23 = A060328(1);
9 + 10 + 12 = 31 = A060328(2);
12 + 14 + 15 = 41 = A060328(3);
18 + 20 + 21 = 59 = A060328(4).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A060328.

Programs

Mathematica

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 *)
Select[Partition[Select[Range[500],CompositeQ],3,1],PrimeQ[Total[#]]&][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 24 2019 *)

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

Formula

By Rosser's theorem, a(2n) > n log n. - Charles R Greathouse IV, Sep 11 2009