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

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

Author

Alexander R. Povolotsky, Aug 21 2025

Keywords

• nonn
• new

Comments

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

			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.
		

Crossrefs

Cf. A000040, A229219, A321578.

Formula

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

Extensions

More terms from David A. Corneth, Aug 22 2025