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%I #10 Apr 04 2015 21:58:26
%S 2,1,3,5,11,15,20,27,36,44,54,64,76,89,102,117,132,149,166,184,204,
%T 228,249,272,296,323,349,376,403,432,461,493,524,556,589,625,660,697,
%U 737,775,814,855,898,943,987,1031,1076,1122,1169,1219,1269,1321,1373,1427
%N 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.
%C The n-th group is chosen so that it is lexicographically earliest.
%C First n-2 numbers are the least previously unused numbers.
%C 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).
%C The n-th number is chosen as the least unused number that meets the two prime conditions.
%C 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.
%e Table begins:
%e 2
%e 1,4
%e 3,6,10
%e 5,7,8,9
%e 11,12,13,14,23
%e 15,16,17,18,19,28
%Y Cf. A092945, A092946, A092947.
%K nonn,tabl
%O 1,1
%A _Amarnath Murthy_, Mar 23 2004
%E Edited and extended by _Ray Chandler_, May 07 2008
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