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%I #14 Mar 14 2014 12:35:36
%S 4,6,8,16,24,33,36,63,48,60,93,140,84,108,132,189,165,144,120,210,297,
%T 168,204,180,276,252,285,288,462,240,372,432,336,300,396,609,360,492,
%U 552,468,564,528,576,504,708,1089,648,480,420,540,768,672,600,816,792
%N Smallest number that can be written in n ways as the sum of two numbers of the form p or 2p, where p is prime.
%H Lei Zhou, <a href="/A238269/b238269.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 is the smallest number that can be written in only one way as the sum of two primes or doubled primes, 4=2+2. So a(1)=4;
%e 6 = 2+2*2 = 3+3, two ways, so a(2)=6;
%e ...
%e 33 = 2+31 = 2*2+29 = 7+2*13 = 2*5+23 = 11+2*11 = 2*7+19, 6 ways. And all numbers smaller than 33 can only be split in 5 or fewer ways. So a(6)=33.
%t target = 55; n = 3; a = {}; sc = 0; Do[AppendTo[a, 0], {i, 1, target}]; While[sc < target, n++; ct = 0; Do[If[((PrimeQ[i]) || (PrimeQ[i/2])) && ((PrimeQ[n - i]) || (PrimeQ[(n - i)/2])), ct++], {i, 2, Floor[n/2]}]; If[ct<=target,If[a[[ct]] == 0, a[[ct]] = n; sc++]]];a
%Y Cf. A001751, A002375, A103151, A238268.
%K nonn
%O 1,1
%A _Lei Zhou_, Feb 21 2014
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