A348549 Number of positive integers with n digits that are the product of two integers ending with 8.

0, 1, 14, 195, 2200, 24013, 255969, 2687317, 27934809, 288342379, 2960920297, 30285890402, 308834717932, 3141625339760, 31895159990436

Offset: 1

Author

Stefano Spezia, Oct 22 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A348548.

Crossrefs

Cf. A052268, A348548.

Cf. A346509 (ending with 1), A346629 (ending with 2), A346952 (ending with 3), A347255 (ending with 4), A337855 (ending with 5), A337856 (ending with 6), A348055 (ending with 7).

Programs

Python

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(8, hi//8+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi))
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Oct 22 2021

Formula

a(n) < A052268(n).

Conjecture: lim_{n->infinity} a(n)/a(n-1) = 10.

Extensions

a(9)-a(10) from Michael S. Branicky, Oct 22 2021

a(11)-a(15) from Martin Ehrenstein, Nov 06 2021