A347255 Number of positive integers with n digits that are the product of two integers ending with 4.

0, 3, 25, 281, 2941, 30596, 315385, 3231664, 32972224, 335346193, 3402373313, 34454358909, 348373701706, 3518101287286, 35491654274101

Offset: 1

Author

Stefano Spezia, Aug 24 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A347253.

Crossrefs

Cf. A017341, A052268, A347253.

Cf. A346509 (ending with 1), A346952 (ending with 3), A337855 (ending with 5), A337856 (ending with 6).

Programs

Python

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(4, hi//4+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, Aug 24 2021

Formula

a(n) < A052268(n).

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

Extensions

a(9)-a(11) from Michael S. Branicky, Aug 25 2021

a(12)-a(15) from Martin Ehrenstein, Sep 29 2021