%I #17 Jan 10 2022 10:45:22
%S 3,11,43,191,797,3259,13267,54049,219277,887707
%N Median of the largest prime dividing the first 10^n numbers greater than 1.
%C A randomly selected number <= 10^n (uniform distribution from 2 to 10^n) has a 50% probability of having a prime factor at least as large as a(n).
%e The largest prime divisors of the nonunit 1-digit numbers are 2, 3, 2, 5, 3, 7, 2 and 3 respectively, with median 3.
%t f[n_Integer(* n must be even so as to find a true median, not an average, and n must be greater than *)] := Block[{cnt, lmt = n/2, p = PrimePi[n/2], q = PrimePi[n]}, cnt = q - p; p--; While[cnt < lmt, cnt = cnt + Floor[n/Prime@ p]; p-- ]; p++; Prime@ p]; MapAt[# + 1 &, Reap[Do[Sow@ f[10^n], {n, 6}]][[-1, -1]], 1]
%Y Cf. A124202, A126283, A281889, A284411.
%K nonn,more
%O 1,1
%A Mark Thornquist (mthornqu(AT)fhcrc.org) and _Robert G. Wilson v_, Dec 15 2006