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Partial sums of n concatenated n times.
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%I #13 Sep 29 2021 10:29:43

%S 1,23,356,4800,60355,727021,8504798,97393686,1097393685,

%T 10101010102107494695,1121212121213218605806,122333333333334430727018,

%U 13253646464646465743858331,1427395060606060607157999745,152942546575757575758673151260,16314558708191919191920289312876

%N Partial sums of n concatenated n times.

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

%F 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)).

%e a(2) = 1 + 22 = 23 is prime.

%e a(6) = 1 + 22 + 333 + 4444 + 55555 + 666666 = 727021 is prime.

%e For what value of n is the next prime a(n)?

%e a(158), which has 474 digits, is prime. - _Harvey P. Dale_, Oct 17 2011

%t Accumulate[FromDigits/@Table[Flatten[IntegerDigits/@PadLeft[{},n,n]], {n,15}]] (* _Harvey P. Dale_, Oct 17 2011 *)

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

%K base,easy,nonn

%O 1,2

%A _Jonathan Vos Post_, May 11 2006