A369385 - OEIS

%I #4 Feb 20 2024 10:29:47

%S 1,4,10,22,34,60,118,112,142,198,270,298,280,364,508,460,588,490,580,

%T 658,858,670,700,994,880,1240,1078,1288,910,1120,1428,1510,1300,1330,

%U 1930,1960,1750,1540,2128,2170,2140,2470,2560,2380,2590,2770,2728,3838,2968,4000

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

%e a(0) = 1 because 1 cannot be written as the sum of two terms in A109611.

%e 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.

%e 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.

%o (Magma) IsSemiprime:=func<n|&+[d[2]: d in Factorization(n)] eq 2>;

%o 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;

%Y Cf. A109611.

%K nonn

%O 0,2

%A _Marius A. Burtea_, Jan 25 2024