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A348547
Number of positive integers with n digits and final digit 9 that are equal to the product of two integers ending with the same digit.
2
1, 4, 49, 524, 5596, 58706, 608886, 6267854, 64180304, 654605898, 6656849267, 67539297095, 683989985496, 6916722312963, 69859080168037
OFFSET
1,2
COMMENTS
a(n) is the number of n-digit numbers in A348545.
FORMULA
a(n) < A052268(n).
a(n) = A346952(n) + A348055(n) - A348546(n).
Conjecture: lim_{n->infinity} a(n)/a(n-1) = 10.
MATHEMATICA
Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Union[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<#<hi&], {n, 8}]
PROG
(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
KEYWORD
nonn,base,hard,more
AUTHOR
Stefano Spezia, Oct 22 2021
EXTENSIONS
a(9) from Michael S. Branicky, Oct 22 2021
a(10)-a(15) from Martin Ehrenstein, Nov 06 2021
STATUS
approved