This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118115 #13 Sep 29 2021 10:29:43
%S A118115 1,23,356,4800,60355,727021,8504798,97393686,1097393685,
%T A118115 10101010102107494695,1121212121213218605806,122333333333334430727018,
%U A118115 13253646464646465743858331,1427395060606060607157999745,152942546575757575758673151260,16314558708191919191920289312876
%N A118115 Partial sums of n concatenated n times.
%D A118115 F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
%F A118115 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 A118115 a(2) = 1 + 22 = 23 is prime.
%e A118115 a(6) = 1 + 22 + 333 + 4444 + 55555 + 666666 = 727021 is prime.
%e A118115 For what value of n is the next prime a(n)?
%e A118115 a(158), which has 474 digits, is prime. - _Harvey P. Dale_, Oct 17 2011
%t A118115 Accumulate[FromDigits/@Table[Flatten[IntegerDigits/@PadLeft[{},n,n]], {n,15}]] (* _Harvey P. Dale_, Oct 17 2011 *)
%Y A118115 Cf. A000461 (concatenate n n times), A004216, A048376, A053422.
%K A118115 base,easy,nonn
%O A118115 1,2
%A A118115 _Jonathan Vos Post_, May 11 2006