A333266 - OEIS

A333266

a(n) is the smallest number k such that for all m >= k there is at least one prime partition of m with prime(n) as least part.

%I #13 Mar 18 2020 18:47:54

%S 4,8,15,24,39,49,67,83,89,115,127,143,163,179,193,223,235,249,271,281,

%T 295,333,349,363,387,403,409,427,461,483,515,535,545,565,595,625,643,

%U 659,685,703,725,733,759,805,813,835,851,895,907,923,937,965,989,1033

%N a(n) is the smallest number k such that for all m >= k there is at least one prime partition of m with prime(n) as least part.

%C a(n) is a term if and only if it is the smallest number such that there exists a prime partition of every m in the interval [a(n), 2*a(n)] with least part prime(n). There is no prime partition of a(n)-1 having prime(n) as least part, and this is the greatest such number.

%e For any k >= 4 there exists a prime partition of k having least part 2, hence a(1)=4.

%Y Cf. A333129, A333238, A330507, A000607, A333259.

%K nonn

%O 1,1

%A _David James Sycamore_, Mar 13 2020

%E More terms from _Alois P. Heinz_, Mar 16 2020