

A128245


Smallest of three consecutive composite numbers whose sum is prime.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



