
COMMENTS

If 1, 3, 7, 13 are taken (rather arbitrarily) as starting terms, then the continuation is 17, 31, 11, 25, 5, 37, 341, 163, 647, 571, 989, 3451, 17669, 206413, 6767, 252289, but no number < 10000000 is suited to continue this sequence further.
There are no further terms. For k to qualify as next term the sums 21+13+k, 7+9+21+13+k and 1+3+7+9+21+13+k have to be prime. One of these sums however is divisible by 3, since 34+k = k+1 (mod 3), 50+k = k+2 (mod 3) and 54+k = k (mod 3).  Klaus Brockhaus, Jul 02 2004


EXAMPLE

1+3+7 = 11, 3+7+9 = 19, 7+9+21 = 37, 9+21+13 = 43, 1+3+7+9+21 = 41, 3+7+9+21+13 = 53 are all prime.
