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A369385
The smallest number k that can be partitioned in n ways as the sum of two numbers from A109611.
0
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
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
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Jan 25 2024
STATUS
approved