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A118115
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Partial sums of n concatenated n times.
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0
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1, 23, 356, 4800, 60355, 727021, 8504798, 97393686, 1097393685, 10101010102107494695, 1121212121213218605806, 122333333333334430727018, 13253646464646465743858331, 1427395060606060607157999745, 152942546575757575758673151260, 16314558708191919191920289312876
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OFFSET
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1,2
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REFERENCES
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F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
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LINKS
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Table of n, a(n) for n=1..16.
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FORMULA
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a(n) = Sum_{i=1..n} A000461(i). a(n) = Sum_{i=1..n} i*(10^(i*L(i))-1)/(10^L(i)-1) where L(i) = A004216(i) + 1 = floor(log_10(10i)).
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EXAMPLE
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a(2) = 1 + 22 = 23 is prime.
a(6) = 1 + 22 + 333 + 4444 + 55555 + 666666 = 727021 is prime.
For what value of n is the next prime a(n)?
a(158), which has 474 digits, is prime. - Harvey P. Dale, Oct 17 2011
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MATHEMATICA
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Accumulate[FromDigits/@Table[Flatten[IntegerDigits/@PadLeft[{}, n, n]], {n, 15}]] (* Harvey P. Dale, Oct 17 2011 *)
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CROSSREFS
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Cf. A000461 (concatenate n n times), A004216, A048376, A053422.
Sequence in context: A021914 A022412 A025946 * A020572 A021884 A101792
Adjacent sequences: A118112 A118113 A118114 * A118116 A118117 A118118
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post, May 11 2006
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STATUS
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approved
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