A369385 The smallest number k that can be partitioned in n ways as the sum of two numbers from A109611.

1, 4, 10, 22, 34, 60, 118, 112, 142, 198, 270, 298, 280, 364, 508, 460, 588, 490, 580, 658, 858, 670, 700, 994, 880, 1240, 1078, 1288, 910, 1120, 1428, 1510, 1300, 1330, 1930, 1960, 1750, 1540, 2128, 2170, 2140, 2470, 2560, 2380, 2590, 2770, 2728, 3838, 2968, 4000

Offset: 0

Author

Marius A. Burtea, Jan 25 2024

Keywords

• nonn

Examples

			a(0) = 1 because 1 cannot be written as the sum of two terms in A109611.
The numbers 2 and 3 cannot be written as the sum of two terms in A109611, and 4 = 2 + 2 = A109611(1) + A109611(1) is the only writing with terms in A109611, so a(1) = 4.
The numbers 5, 6, 7, 8, 9 can be written as the sum of two terms in A109611 in at most one way and 10 = 3 + 7 = A109611(2) + A109611(4) and 10 = 5 + 5 = A109611(3) + A109611(3), so a(2) = 10.
		

Crossrefs

Cf. A109611.

Programs

Magma

IsSemiprime:=func;
ch:=func; b:=[n: n in [1..4000] |ch(n)]; a:=[]; for n in [0..47] do k:=1; while #RestrictedPartitions(k, 2, Set(b)) ne n do k:=k+1; end while; Append(~a,k); end for; a;