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A117054
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Number of ordered ways of writing n = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
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2
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0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 0, 3, 0, 1, 1, 3, 0, 4, 0, 1, 0, 2, 0, 3, 1, 3, 0, 3, 0, 3, 0, 2, 0, 2, 0, 5, 1, 2, 0, 3, 0, 6, 0, 1, 0, 4, 0, 3, 0, 1, 1, 5, 0, 5, 0, 3, 0, 3, 0, 4, 0, 2, 0, 3, 0, 7, 1, 3, 0, 3, 0, 6, 0, 2, 0, 4, 0, 6, 0, 2, 0, 4, 0, 5, 1, 3, 0, 5, 0, 3, 0, 3, 0, 5, 0, 8, 0, 1
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OFFSET
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0,9
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COMMENTS
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Based on a posting by Zhi-Wei Sun to the Number Theory Mailing List, Mar 23 2008, where he conjectures that a(2n+1) > 0 for n >= 2.
Zhi-Wei Sun has offered a monetary reward for settling this conjecture.
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LINKS
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MAPLE
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t0:=array(0..300); for n from 0 to 300 do t0[n]:=0; od:
t1:=[seq(ithprime(i), i=1..70)]; t2:=[seq(n*(n+1), n=1..30)];
for i from 1 to 70 do for j from 1 to 30 do k:=t1[i]+t2[j]; if k <= 300 then t0[k]:=t0[k]+1; fi; od: od:
t3:=[seq(t0[n], n=1..300)];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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