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A118115 Partial sums of n concatenated n times. 0
1, 23, 356, 4800, 60355, 727021, 8504798, 97393686, 1097393685, 10101010102107494695, 1121212121213218605806, 122333333333334430727018, 13253646464646465743858331, 1427395060606060607157999745 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A000461 Concatenate n n times.

REFERENCES

F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

LINKS

Table of n, a(n) for n=1..14.

FORMULA

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[log10(10i)]

EXAMPLE

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.  [From Harvey P. Dale, Oct 17 2011]

MATHEMATICA

Accumulate[FromDigits/@Table[Flatten[IntegerDigits/@PadLeft[{}, n, n]], {n, 15}]] (* Harvey P. Dale, Oct 17 2011 *)

CROSSREFS

Cf. A000461, A004216, A048376, A053422.

Sequence in context: A021914 A022412 A025946 * A020572 A021884 A101792

Adjacent sequences:  A118112 A118113 A118114 * A118116 A118117 A118118

KEYWORD

base,easy,nonn

AUTHOR

Jonathan Vos Post, May 11 2006

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)