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 A309440 #24 Sep 14 2019 22:59:48 %S A309440 1,2,16,160,1591,15905,159041,1590405,15904042,159040419,1590404183, %T A309440 15904041824,159040418240,1590404182399,15904041823989, %U A309440 159040418239888,1590404182398875,15904041823988748,159040418239887480,1590404182398874791,15904041823988747910,159040418239887479099 %N A309440 The number of digits of the greatest product from addends that sum up to 10^n. %F A309440 a(n) = 1 + floor(log_10(36) + 10*log_10(27)*R_(n-1)), R_k being the k-th repunit, i.e., 111...111 with only digit 1 appearing k times. %e A309440 The greatest product of numbers that sum up to 10 is 2*2*3*3 = 36 which has 2 digits. Thus a(1) = 2. %e A309440 The greatest product of numbers that sum up to 100 is 2*2*3^(32) ~ 7.4*10^15 which has 16 digits. Hence a(2) = 16. %e A309440 The greatest product of numbers that sum up to 1000 is 2*2*3^(332) ~ 1.0*10^159 which has 160 digits. Therefore a(3) = 160. %o A309440 (PARI) a(n) = 1 + floor(log(4)/log(10) + ((10^n-1)/3-1)*log(3)/log(10)); \\ _Jinyuan Wang_, Aug 03 2019 %Y A309440 Cf. A000792. %K A309440 nonn,base %O A309440 0,2 %A A309440 _Lekraj Beedassy_, Aug 03 2019