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
Keywords
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
Crossrefs
Cf. A164024.
Programs
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Mathematica
Table[Max[Select[IntegerPartitions[n,{3}],AllTrue[#,PrimeQ]&][[;;,2]]],{n,6,90}] (* Harvey P. Dale, Jan 31 2025 *)