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

0,2

Links

Table of n, a(n) for n=0..49.

Example

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.

Prog

(Magma) IsSemiprime:=func<n|&+[d[2]: d in Factorization(n)] eq 2>;
ch:=func<p|IsPrime(p) and (IsPrime(p+2) or IsSemiprime(p+2))>; 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;

Crossrefs

Cf. A109611.

Sequence in context: A250398 A112774 A352296 * A227225 A008178 A009891

Adjacent sequences: A369382 A369383 A369384 * A369386 A369387 A369388

Keyword

nonn

Author

Marius A. Burtea, Jan 25 2024

Status

approved