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

%I A335285 #14 Jun 04 2020 02:04:06
%S A335285 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,
%T A335285 23,29,23,31,29,31,31,31,31,37,31,37,37,41,37,43,41,43,43,47,43,47,47,
%U A335285 47,47,53,47,53,53,53,53,59,53,61,59,61,61,61,61,67,61,67
%N A335285 a(n) is the greatest possible greatest part of any partition of n into prime parts.
%C A335285 For n odd, a(n) is the greatest prime <= n; for n even > 2, a(n) is the greatest prime < n-1.
%C A335285 For composite n = p + 1, p does not appear since 2 is the smallest prime. - _Michael De Vlieger_, May 31 2020
%H A335285 Michael De Vlieger, <a href="/A335285/b335285.txt">Table of n, a(n) for n = 2..10000</a>
%H A335285 Michael De Vlieger, <a href="/A335285/a335285.png">Plot of greatest primes of prime partitions of n</a> for 2 <= n <= 41; this sequence is the greatest prime shown in each row of the diagram.
%e A335285 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).
%e A335285 a(12) = 7 (greatest prime < 11).
%t A335285 Array[Max@ Select[IntegerPartitions[#], AllTrue[#, PrimeQ] &][[All, 1]] &, 68, 2] (* _Michael De Vlieger_, May 30 2020 *)
%t A335285 Array[Prime[PrimePi@ # - Boole[And[PrimeQ[# - 1], # != 3]]] &, 68, 2] (* _Michael De Vlieger_, May 31 2020 *)
%Y A335285 Cf. A331634, A335106.
%K A335285 nonn
%O A335285 2,1
%A A335285 _David James Sycamore_, _Michael De Vlieger_ May 30 2020