cp's OEIS Frontend

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

%I A369385 #4 Feb 20 2024 10:29:47
%S A369385 1,4,10,22,34,60,118,112,142,198,270,298,280,364,508,460,588,490,580,
%T A369385 658,858,670,700,994,880,1240,1078,1288,910,1120,1428,1510,1300,1330,
%U A369385 1930,1960,1750,1540,2128,2170,2140,2470,2560,2380,2590,2770,2728,3838,2968,4000
%N A369385 The smallest number k that can be partitioned in n ways as the sum of two numbers from A109611.
%e A369385 a(0) = 1 because 1 cannot be written as the sum of two terms in A109611.
%e A369385 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 A369385 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 A369385 (Magma) IsSemiprime:=func<n|&+[d[2]: d in Factorization(n)] eq 2>;
%o A369385 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 A369385 Cf. A109611.
%K A369385 nonn
%O A369385 0,2
%A A369385 _Marius A. Burtea_, Jan 25 2024