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%I #24 Dec 25 2020 11:08:59
%S 10,119,583,1139,1415,565,1057,1713,817,2105,1717,1099,3629,1315,3263,
%T 3046,5105,1807,1849,1915,1959,3385,3589,5293,7343,2569,6209,2785,
%U 2841,3898,5029,3085,3139,3193,7697,3403,3487,3561,8551,3785,6439,10606,9841,4319,5834,16589,11009,8049,4885
%N Partition the primes into groups with semiprime sums: {2,3,5},{7,11,13,17,19,23,29}, {31,37,41,43,47,53,59,61,67,71,73},.... The sequence lists the sums of the groups.
%C Lengths of groups: 3, 7, 11, 11, 9, 3, 5, 7, 3, 7, 5, 3, 9, 3, 7, 6, 9, 3, 3, 3, 3, 5, 5, 7, 9, 3, 7, 3, 3, 4, 5, 3, 3, 3, 7, 3, 3, 3, 7, 3, 5, 8, 7, 3, 4, 11, 7, 5, 3, 6, 3, 7, 3, 3, 3, 3, 3, 3, 7, 3, 3, 7, 3, 5, 7, 3, 5, 7, 5, 7, 13, 5, 5, 17, 6, 11, 3, 15, 3, 3, 5.
%C Minimal length is 3 but what about maximal length of groups?
%e a(1) = 10 because 2 + 3 + 5 = 2*5 = A001358(4);
%e a(2) = 119 because 7 + 11 + 13 + 17 + 19 + 23 + 29 = 7*17 = A001358(39).
%t s = {10}; t = p = 7; Do[While[2 != PrimeOmega[t],
%t t = t + (p = NextPrime[p])]; AppendTo[s, t]; t = p = NextPrime[p], {80}]; s
%Y Cf. A000040, A001358, A188651.
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 19 2020
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