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A347748
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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.
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2
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0, 1, 12, 159, 1859, 20704, 223525, 2370684, 24842265, 258128126, 2665475963
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OFFSET
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1,3
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COMMENTS
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a(n) is the number of n-digit numbers in A347746.
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LINKS
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FORMULA
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Conjecture: lim_{n->infinity} a(n)/a(n-1) = 10.
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MATHEMATICA
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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}]
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PROG
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(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) & 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))
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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