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

58, 6610, 668843, 66965113, 6697324753, 669740590290, 66974140069358, 6697414817000983, 669741489800555031, 66974149061059480123

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = 9*10^(2n-1) - 10^n - Sum_{k=10^(n-1)+1..10^n-1} ceiling(10^(2n-1)/k).

a(n) ~ (9-log(10))*10^(2n-1).

Example

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).

Prog

(Python)
import math
ende = 1
for i in range(1, 10):
   anz = 0
   for a in range(ende, 10*ende):
      z = math.ceil((ende*ende*10)/a)
      if z < ende*10:
         anz = anz + ende*10 - z
   ende = ende*10
   print(i, anz)
(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

Crossrefs

Cf. A174425.

Sequence in context: A042625 A250919 A282438 * A128934 A173955 A243466

Adjacent sequences: A308388 A308389 A308390 * A308392 A308393 A308394

Keyword

nonn,base,more

Author

Reiner Moewald, May 23 2019

Status

approved