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A338975
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.
0
10, 119, 583, 1139, 1415, 565, 1057, 1713, 817, 2105, 1717, 1099, 3629, 1315, 3263, 3046, 5105, 1807, 1849, 1915, 1959, 3385, 3589, 5293, 7343, 2569, 6209, 2785, 2841, 3898, 5029, 3085, 3139, 3193, 7697, 3403, 3487, 3561, 8551, 3785, 6439, 10606, 9841, 4319, 5834, 16589, 11009, 8049, 4885
OFFSET
1,1
COMMENTS
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.
Minimal length is 3 but what about maximal length of groups?
EXAMPLE
a(1) = 10 because 2 + 3 + 5 = 2*5 = A001358(4);
a(2) = 119 because 7 + 11 + 13 + 17 + 19 + 23 + 29 = 7*17 = A001358(39).
MATHEMATICA
s = {10}; t = p = 7; Do[While[2 != PrimeOmega[t],
t = t + (p = NextPrime[p])]; AppendTo[s, t]; t = p = NextPrime[p], {80}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Dec 19 2020
STATUS
approved