A188651 -id:A188651 - cp's OEIS frontend

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.

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

Zak Seidov, Dec 19 2020

nonn

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?

			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).

Cf. A000040, A001358, A188651.

s = {10}; t = p = 7; Do[While[2 !=  PrimeOmega[t],
t = t + (p = NextPrime[p])]; AppendTo[s, t]; t = p = NextPrime[p], {80}]; s

cp's OEIS Frontend

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.

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