A355250 Largest prime appearing among the "middle parts" of the partitions of n into (exactly) 3 prime parts.

2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 11, 13, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 17, 19, 19, 19, 13, 19, 23, 23, 19, 23, 19, 23, 23, 23, 23, 23, 19, 23, 29, 29, 29, 29, 31, 31, 23, 31, 29, 31, 31, 31, 29, 31, 31, 31, 37, 37, 29, 37

Offset: 6

Author

Wesley Ivan Hurt, Jun 25 2022

Keywords

• nonn

Examples

			a(17) = 7; of the 4 ways to write 17 as the sum of 3 primes, 7 is the largest "middle" part: 2+2+13 = 3+3+11 = 3+7+7 = 5+5+7.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 6..1000
• Index entries for sequences related to partitions

Crossrefs

Cf. A164024.

Programs

Mathematica

Table[Max[Select[IntegerPartitions[n,{3}],AllTrue[#,PrimeQ]&][[;;,2]]],{n,6,90}] (* Harvey P. Dale, Jan 31 2025 *)