A096102 a(1) = 1, a(2) = 3; for n > 2: a(n) = smallest (odd) number not occurring earlier such that the sum of each section of odd length >=3 is prime.

1, 3, 7, 9, 21, 13

Offset

1,2

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

Links

Table of n, a(n) for n=1..6.

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.

Crossrefs

Cf. A096100, A096101.

Sequence in context: A304128 A304539 A306124 * A316157 A045797 A118555

Adjacent sequences: A096099 A096100 A096101 * A096103 A096104 A096105

Keyword

nonn

Author

Amarnath Murthy, Jun 24 2004

Extensions

Edited and corrected by Klaus Brockhaus, Jun 29 2004

Status

approved