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A308391 Number of ordered pairs of n-digit positive integers the product of which is a 2n-digit integer. 0
58, 6610, 668843, 66965113, 6697324753, 669740590290, 66974140069358, 6697414817000983, 669741489800555031, 66974149061059480123 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)