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A339772
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Number of Goldbach partitions of 2n whose parts have the same number of decimal digits.
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0
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0, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 2, 2, 4, 2, 3, 5, 2, 3, 4, 1, 4, 5, 3, 3, 5, 3, 4, 7, 3, 3, 8, 3, 4, 6, 3, 5, 7, 3, 4, 6, 4, 4, 6, 3, 3, 7, 2, 2, 6, 2, 3, 4, 3, 2, 3, 3, 3, 3, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} [floor(log_10(k)) = floor(log_10(2*n-k))] * c(k) * c(2*n-k), where [ ] is the Iverson bracket and c is the prime characteristic (A010051).
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EXAMPLE
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a(7) = 1; 2*7 = 14 has two Goldbach partitions, (11,3) and (7,7). Since (7,7) is the only one whose parts have the same number of decimal digits, a(7) = 1.
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MATHEMATICA
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Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]) KroneckerDelta[Floor[Log10[i]], Floor[Log10[2 n - i]]], {i, n}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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