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A067187
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Numbers that can be expressed as the sum of two primes in exactly one way.
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17
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4, 5, 6, 7, 8, 9, 12, 13, 15, 19, 21, 25, 31, 33, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265, 271
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OFFSET
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1,1
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COMMENTS
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All primes + 2 are terms of this sequence. Is 12 the last even term? - Frank Ellermann, Jan 17 2002
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LINKS
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EXAMPLE
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4 is a term as 4 = 2+2, 15 is a term as 15 = 13+2.
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MAPLE
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g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j), j=1..80): gser:=series(g, x=0, 280): a:=proc(n) if coeff(gser, x^n)=1 then n else fi end: seq(a(n), n=1..272); # Emeric Deutsch, Apr 03 2006
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MATHEMATICA
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cQ[n_]:=Module[{c=0}, Do[If[PrimeQ[n-i]&&PrimeQ[i], c++], {i, 2, n/2}]; c==1]; Select[Range[4, 271], cQ[#]&] (* Jayanta Basu, May 22 2013 *)
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CROSSREFS
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Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), this sequence (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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