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%I #24 May 28 2023 20:51:33
%S 5,16,10,24,18,17,36,26,23,28,48,31,29,34,41,60,35,33,-1,47,58,78,39,
%T 37,40,70,64,77,84,80,41,55,53,72,87,100
%N Array read by descending antidiagonals. A(n,k), n > 1 and k > 0, is the least m such that the number of partitions of m into n distinct prime parts is exactly k, or -1 if no such number exists.
%e A(2, 1) = 5 = 2 + 3, because 5 is the least number for which there exists exactly one partition into 2 distinct primes.
%e A(2, 2) = 16 = 3 + 13 = 5 + 11, because 16 is the least number for which there exist exactly 2 partitions into 2 distinct primes.
%e Array begins:
%e 2: 5, 16, 24, 36, 48, 60, 78, 84, ...
%e 3: 10, 18, 26, 31, 35, 39, 80, ...
%e 4: 17, 23, 29, 33, 37, 41, ...
%e 5: 28, 34, -1, 40, 55, ...
%e 6: 41, 47, 70, 53, ...
%e 7: 58, 64, 72, ...
%e 8: 77, 87, ...
%e 9: 100, ...
%Y Cf. A000586, A000607, A358010.
%K sign,more
%O 2,1
%A _Jean-Marc Rebert_, May 28 2023