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A065577
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Number of Goldbach partitions of 10^n.
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10
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2, 6, 28, 127, 810, 5402, 38807, 291400, 2274205, 18200488, 149091160, 1243722370, 10533150855, 90350630388
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OFFSET
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1,1
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COMMENTS
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Number of ways of writing 10^n as the sum of two odd primes, when the order does not matter.
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LINKS
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FORMULA
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EXAMPLE
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a(1)=2 because 10 = 3+7 = 5+5;
a(2)=6 because 100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53; ...
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{c = 0, lmt = n/2, p = 3}, While[p <= lmt, If[ PrimeQ[n - p], c++ ]; p = NextPrim@p]; c]; Array[f, 10] (* Robert G. Wilson v, Nov 01 2006 *)
a[n]:=Length[Select[n - Prime[Range[PrimePi[n/2]]], PrimeQ]]; Table[a[n], {n, 10^3, 10^3}] (* Luciano Ancora, Mar 16 2015 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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a(14) from Huang Yuanbing (bailuzhou(AT)163.com), Dec 24 2009
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STATUS
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approved
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