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

1,3

Comments

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).

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

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}]

Prog

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

Crossrefs

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

Sequence in context: A100790 A055250 A038740 * A163614 A207318 A293042

Adjacent sequences: A225425 A225426 A225427 * A225429 A225430 A225431

Keyword

nonn,base

Author

T. D. Noe, Jun 21 2013

Extensions

a(10) from Hugo Pfoertner, May 12 2023

Status

approved