A118115 Partial sums of n concatenated n times.

1, 23, 356, 4800, 60355, 727021, 8504798, 97393686, 1097393685, 10101010102107494695, 1121212121213218605806, 122333333333334430727018, 13253646464646465743858331, 1427395060606060607157999745, 152942546575757575758673151260, 16314558708191919191920289312876

Offset: 1

Author

Jonathan Vos Post, May 11 2006

Keywords

• base
• easy
• nonn

Examples

			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
		

References

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

Crossrefs

Cf. A000461 (concatenate n n times), A004216, A048376, A053422.

Programs

Mathematica

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

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(log_10(10i)).