cp's OEIS Frontend

A225428 Number of numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 2.

%I A225428 #10 May 12 2023 12:27:53
%S A225428 0,1,9,47,212,1232,6592,31145,129587,597959
%N A225428 Number of numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 2.
%C A225428 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).
%e A225428 The only two-digit number is 88, whose square is 7744.
%t A225428 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}]
%o A225428 (Python)
%o A225428 from collections import Counter
%o A225428 def passes(x): return set(Counter(str(x**2)).values()) == {2}
%o A225428 def afull():
%o A225428     c = 0
%o A225428     for n in range(1, 11):
%o A225428         c += sum(1 for x in range(10**(n-1), 10**n) if passes(x))
%o A225428         print(c, end=", ")
%o A225428 afull() # _Michael S. Branicky_, May 12 2023
%Y A225428 Cf. A052049, A052050, A225429 (first differences), A226796 (single digits).
%K A225428 nonn,base
%O A225428 1,3
%A A225428 _T. D. Noe_, Jun 21 2013
%E A225428 a(10) from _Hugo Pfoertner_, May 12 2023