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A308391 Number of ordered pairs of n-digit positive integers the product of which is a 2n-digit integer.

%I A308391 #21 Jul 14 2019 13:31:30
%S A308391 58,6610,668843,66965113,6697324753,669740590290,66974140069358,
%T A308391 6697414817000983,669741489800555031,66974149061059480123
%N A308391 Number of ordered pairs of n-digit positive integers the product of which is a 2n-digit integer.
%F A308391 a(n) = 9*10^(2n-1) - 10^n - Sum_{k=10^(n-1)+1..10^n-1} ceiling(10^(2n-1)/k).
%F A308391 a(n) ~ (9-log(10))*10^(2n-1).
%e A308391 a(1)=58 since we get the following pairs: (2, 5), ..., (2, 9), (3, 4), ..., (3, 9), (4, 3), ..., (4, 9), (5, 2), ..., (5, 9), (6, 2), ..., (6, 9), (7, 2), ..., (7, 9), (8, 2), ..., (8, 9), (9, 2), ..., (9, 9).
%o A308391 (Python)
%o A308391 import math
%o A308391 ende = 1
%o A308391 for i in range(1,10):
%o A308391    anz = 0
%o A308391    for a in range(ende, 10*ende):
%o A308391       z = math.ceil((ende*ende*10)/a)
%o A308391       if z < ende*10:
%o A308391          anz = anz + ende*10 - z
%o A308391    ende = ende*10
%o A308391    print(i, anz)
%o A308391 (PARI) a(n) = 9*10^(2*n-1) - 10^n - sum(k=10^(n-1)+1, 10^n-1, ceil(10^(2*n-1)/k)); \\ _Michel Marcus_, Jun 25 2019
%Y A308391 Cf. A174425.
%K A308391 nonn,base,more
%O A308391 1,1
%A A308391 _Reiner Moewald_, May 23 2019