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A225428
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Number of numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 2.
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5
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OFFSET
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1,3
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COMMENTS
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The first 47 terms of A052049 and A052050 list the numbers x. Note that n-digit numbers x must be greater than floor(sqrt(10) * 10^(n-1)). All terms after a(10) will equal a(10).
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LINKS
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EXAMPLE
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The only two-digit number is 88, whose square is 7744.
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MATHEMATICA
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cnt = 0; Table[x = Floor[Sqrt[10] * 10^(n-1)]; While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {2}, cnt++]; x++]; cnt, {n, 6}]
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PROG
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(Python)
from collections import Counter
def passes(x): return set(Counter(str(x**2)).values()) == {2}
def afull():
c = 0
for n in range(1, 11):
c += sum(1 for x in range(10**(n-1), 10**n) if passes(x))
print(c, end=", ")
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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