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

1,1

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A060328.

Sequence in context: A136360 A023483 A023042 * A117714 A245685 A315957

Adjacent sequences: A128242 A128243 A128244 * A128246 A128247 A128248

Keyword

nonn

Author

Zak Seidov, May 03 2007

Status

approved