A335285 a(n) is the greatest possible greatest part of any partition of n into prime parts.

2, 3, 2, 5, 3, 7, 5, 7, 7, 11, 7, 13, 11, 13, 13, 17, 13, 19, 17, 19, 19, 23, 19, 23, 23, 23, 23, 29, 23, 31, 29, 31, 31, 31, 31, 37, 31, 37, 37, 41, 37, 43, 41, 43, 43, 47, 43, 47, 47, 47, 47, 53, 47, 53, 53, 53, 53, 59, 53, 61, 59, 61, 61, 61, 61, 67, 61, 67

Offset: 2

Author

David James Sycamore, Michael De Vlieger May 30 2020

Keywords

• nonn

Comments

For n odd, a(n) is the greatest prime <= n; for n even > 2, a(n) is the greatest prime < n-1.

For composite n = p + 1, p does not appear since 2 is the smallest prime. - Michael De Vlieger, May 31 2020

Examples

			a(9) = 7, the greatest prime < 9 (prime partitions of 9 are: [2,7], [2,2,5], [2,2,2,3] and [3,3,3], in which 7 is greatest of greatest parts).
a(12) = 7 (greatest prime < 11).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..10000
• Michael De Vlieger, Plot of greatest primes of prime partitions of n for 2 <= n <= 41; this sequence is the greatest prime shown in each row of the diagram.

Crossrefs

Cf. A331634, A335106.

Programs

Mathematica

Array[Max@ Select[IntegerPartitions[#], AllTrue[#, PrimeQ] &][[All, 1]] &, 68, 2] (* Michael De Vlieger, May 30 2020 *)
Array[Prime[PrimePi@ # - Boole[And[PrimeQ[# - 1], # != 3]]] &, 68, 2] (* Michael De Vlieger, May 31 2020 *)