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A238269
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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.
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1
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4, 6, 8, 16, 24, 33, 36, 63, 48, 60, 93, 140, 84, 108, 132, 189, 165, 144, 120, 210, 297, 168, 204, 180, 276, 252, 285, 288, 462, 240, 372, 432, 336, 300, 396, 609, 360, 492, 552, 468, 564, 528, 576, 504, 708, 1089, 648, 480, 420, 540, 768, 672, 600, 816, 792
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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;
6 = 2+2*2 = 3+3, two ways, so a(2)=6;
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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.
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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