login
a(n) = n - prevprime(n - 1), where prevprime(n) is the largest prime < n.
0

%I #5 May 11 2019 02:22:31

%S 2,2,3,2,3,2,3,4,5,2,3,2,3,4,5,2,3,2,3,4,5,2,3,4,5,6,7,2,3,2,3,4,5,6,

%T 7,2,3,4,5,2,3,2,3,4,5,2,3,4,5,6,7,2,3,4,5,6,7,2,3,2,3,4,5,6,7,2,3,4,

%U 5,2,3,2,3,4,5,6,7,2,3,4,5,2,3,4,5,6

%N a(n) = n - prevprime(n - 1), where prevprime(n) is the largest prime < n.

%C a(n) is the smallest part appearing in the single partition of n into two parts whose largest prime part is < n - 1.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = n - A151799(n - 1).

%e a(11) = 4; 11 has 5 partitions into 2 parts: (10,1), (9,2), (8,3), (7,4) and (6,5). The single partition containing the largest prime part < 10 is (7,4) and 4 is the smallest part in this partition, so a(11) = 4.

%t Table[n - NextPrime[n - 1, -1], {n, 4, 100}]

%Y Cf. A151799.

%K nonn,easy

%O 4,1

%A _Wesley Ivan Hurt_, May 10 2019