A226796 -id:A226796 - 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.

0, 1, 9, 47, 212, 1232, 6592, 31145, 129587, 597959

Offset: 1

T. D. Noe, Jun 21 2013

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).

			The only two-digit number is 88, whose square is 7744.

Cf. A052049, A052050, A225429 (first differences), A226796 (single digits).

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}]

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=", ")
afull() # Michael S. Branicky, May 12 2023

a(10) from Hugo Pfoertner, May 12 2023

A226797 Number of n-digit numbers x such that the digits of x^2 occur with frequency 1.

Original entry on oeis.org

10, 49, 162, 220, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

T. D. Noe, Jun 21 2013

After a(5), all terms are 0.

			All numbers 0 to 9 have squares containing only digits of frequency 1: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81.

Cf. A225428, A226796.

cnt = 0; x = 0; t2 = Table[While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {1}, cnt++]; x++]; cnt, {n, 5}]; Differences[Join[{0}, t2]]

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.

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