A390531 a(n) is the smallest number k such that the first k prime numbers can be partitioned into n subsets of equal sums.

1, 3, 10, 11, 17, 57, 22, 29, 30, 51, 53, 97, 49, 47, 103, 79, 98, 113, 70, 85, 84, 87, 80, 99, 89, 117, 187, 115, 112, 195, 111, 171, 175, 151, 180, 163, 222

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Dean D. Ballard, Example partitions for a(1)..a(37) with justifications.

Sean A. Irvine, Java program (github)

Formula

a(n) >= A053050(n). - Michael S. Branicky, Nov 09 2025

Example

a(2) = 3 because the first 3 primes, {2, 3, 5}, can be partitioned into {2, 3} and {5}, which both have a sum of 5.
a(3) = 10 because the first 10 primes, {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}, can be partitioned into {3, 11, 29}, {7, 13, 23}, and {2, 5, 17, 19}, all of which have a sum of 43.

Crossrefs

Cf. A007504, A053050, A331479, A331541.

Sequence in context: A169939 A357627 A073108 * A352776 A395645 A255160

Adjacent sequences: A390528 A390529 A390530 * A390532 A390533 A390534

Keyword

nonn,more,nice

Author

Dean D. Ballard, Nov 09 2025

Status

approved