A348546 Number of positive integers with n digits that are equal both to the product of two integers ending with 3 and to that of two integers ending with 7.

0, 0, 8, 129, 1771, 21802, 252793, 2826973, 30872783

Offset: 1

Author

Stefano Spezia, Oct 22 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A348544.

Crossrefs

Cf. A052268, A346950, A346952, A348054, A348055, A348544, A348547.

Programs

Mathematica

Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Intersection[Union@Flatten@Table[a*b, {a, 3, Floor[hi/3], 10}, {b, a, Floor[hi/a], 10}], Union@Flatten@Table[a*b, {a, 7, Floor[hi/7], 10}, {b, a, Floor[hi/a], 10}]], lo<#
				

Python

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(3, hi//3+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi) & set(a*b for a in range(7, hi//7+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).

a(n) = A346952(n) + A348055(n) - A348547(n).

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

Extensions

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