%I #12 Jan 06 2024 20:08:27

%S 0,1,12,159,1859,20704,223525,2370684,24842265,258128126,2665475963

%N Number of positive integers with n digits that are equal both to the product of two integers ending with 4 and to that of two integers ending with 6.

%C a(n) is the number of n-digit numbers in A347746.

%F a(n) < A052268(n).

%F a(n) = A337856(n) + A347255(n) - A347749(n).

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

%t Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Intersection[Union@Flatten@Table[a*b, {a, 4, Floor[hi/4], 10}, {b, a, Floor[hi/a], 10}],Union@Flatten@Table[a*b, {a, 6, Floor[hi/6], 10}, {b, a, Floor[hi/a], 10}]], lo<#<hi&], {n,8}]

%o (Python)

%o def a(n):

%o lo, hi = 10**(n-1), 10**n

%o 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) & set(a*b for a in range(6, hi//6+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi))

%o print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, Oct 06 2021

%Y Cf. A017341, A052268, A324297, A337856, A347253, A347255, A347746, A347749.

%K nonn,base,hard,more

%O 1,3

%A _Stefano Spezia_, Sep 12 2021

%E a(9)-a(10) from _Michael S. Branicky_, Oct 06 2021

%E a(11) from _Frank A. Stevenson_, Jan 06 2024