1,2

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

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.

Cf. A096100, A096101.

Sequence in context: A073573 A059621 A034926 this_sequence A045797 A118555 A056652

Adjacent sequences: A096099 A096100 A096101 this_sequence A096103 A096104 A096105

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 24 2004

Edited and corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 29 2004