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

1,1

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?

Links

Table of n, a(n) for n=1..49.

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

Cf. A000040, A001358, A188651.

Sequence in context: A284331 A145510 A160601 * A327653 A024128 A289215

Adjacent sequences: A338972 A338973 A338974 * A338976 A338977 A338978

Keyword

nonn

Author

Zak Seidov, Dec 19 2020

Status

approved