A092944 Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product + 1 is prime. Sequence contains the first member of the groups.

2, 1, 3, 5, 11, 15, 20, 27, 36, 44, 54, 64, 76, 89, 102, 117, 132, 149, 166, 184, 204, 228, 249, 272, 296, 323, 349, 376, 403, 432, 461, 493, 524, 556, 589, 625, 660, 697, 737, 775, 814, 855, 898, 943, 987, 1031, 1076, 1122, 1169, 1219, 1269, 1321, 1373, 1427

Offset: 1

Author

Amarnath Murthy, Mar 23 2004

Keywords

• nonn
• tabl

Comments

The n-th group is chosen so that it is lexicographically earliest.

First n-2 numbers are the least previously unused numbers.

The (n-1)st number is chosen with the additional condition that if the product is odd, the sum is also odd (to avoid an impossible situation in picking the n-th number).

The n-th number is chosen as the least unused number that meets the two prime conditions.

In the 3rd group, 6 is selected as the 2nd number rather than 5, else no 3rd number could be found to meet the prime conditions.

Examples

			Table begins:
2
1,4
3,6,10
5,7,8,9
11,12,13,14,23
15,16,17,18,19,28
		

Crossrefs

Cf. A092945, A092946, A092947.

Extensions

Edited and extended by Ray Chandler, May 07 2008