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A123119
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Number of digits in sum of first n primes (A007504).
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0
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1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Since A007504(n) has the asymptotic expression ~ n^2 * log(n) / 2, we have a(n) has the asymptotic expression n^2 * log(n) / 2 = floor[log10(10* n^2 * log(n) / 2)] = floor[log10(5* n^2 * log(n))] = floor[log10(5) + log10(n^2) + log10(log(n))] = floor[0.698970004 + 2*log10(n) + log10(log(n))]. What is the smallest n such that a(n) = 5, 6, 7, ...?
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FORMULA
| a(n) = A055642(A007504(n)) = floor[log10(10*A007504(n))] = A004216(A007504(n))+1 = A004218(A007504(n)+1).
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EXAMPLE
| a(3) = 2 because 2 + 3 + 5 = 10 has 2 digits in its decimal expansion.
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MATHEMATICA
| f[n_] := Floor[ Log[10, Sum[Prime@i, {i, n}]] + 1]; Array[f, 105] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A000040, A000041, A004216, A004218, A034386, A055642, A111287.
Sequence in context: A185679 A080342 A081604 * A099396 A126235 A191228
Adjacent sequences: A123116 A123117 A123118 * A123120 A123121 A123122
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KEYWORD
| base,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 28 2006
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EXTENSIONS
| More terms from Robert G. Wilson v Oct 05 2006
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