A229219 -id:A229219 - cp's OEIS frontend

A387215 a(n) is the smallest k such that, for any m >= k, m is a sum of exactly n distinct primes.

18, 31, 42, 61, 84, 103, 138, 163, 204, 245, 294, 335, 390, 449, 516, 575, 648, 725, 804, 885, 978, 1067, 1164, 1277, 1374, 1493, 1608, 1739, 1866, 2003, 2142, 2291, 2436, 2603, 2760, 2933, 3096, 3281, 3468, 3647, 3858, 4055, 4248, 4457, 4684, 4913, 5142, 5375, 5604

Offset: 3

David A. Corneth, Aug 22 2025

In computation it is assumed that if for any m where a(n) = k <= m <= k + 3*n we have m is the sum of n distinct positive integers then a(n) = k.

			a(3) = 18 as 17 is not the sum of 3 distinct primes but any integer m where 18 <= m <= 27 is the sum of 3 distinct primes. It is therefore assumed that a(3) = 18.

Cf. A002375, A229219, A387198.

A386515 a(n) is the largest number of distinct primes in a partition of prime(n) into primes.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15

Offset: 1

Alexander R. Povolotsky, Aug 21 2025

For each prime number prime(n) find all sums of smaller prime numbers which add up to this prime number. Among those sums find the largest number of distinct primes.

			Examples of such partitions for n = 3..11:
  prime(3) = 5 = 2 + 3 which gives a(3) = 2;
  prime(4) = 7 = 2 + 5 which gives a(4) = 2;
  prime(5) = 11 = 2 + 2 + 2 + 2 + 3 = 3 + 3 + 5 which gives a(5)=2;
  prime(6) = 13 = 2 + 3 + 5 + 3 which gives a(6)=3;
  prime(7) = 17 = 2 + 3 + 5 + 7 which gives a(7)=4;
  prime(8) = 19 = 2 + 3 + 5 + 7 + 2 which gives a(8)=4;
  prime(9) = 23 = 2 + 3 + 5 + 13 which gives a(9)=4;
  prime(10) = 29 = 2 + 3 + 5 + 19 which gives a(10)=4;
  prime(11) = 31 = 2 + 3 + 5 + 7 + 7 + 7 which gives a(11)=4.

Cf. A000040, A229219, A321578.

a(n) <= A321578(n). - David A. Corneth, Aug 22 2025

More terms from David A. Corneth, Aug 22 2025

cp's OEIS Frontend

A387215 a(n) is the smallest k such that, for any m >= k, m is a sum of exactly n distinct primes.

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