A366940 a(n) is the number of positive squares with n digits, all distinct.

3, 6, 13, 36, 66, 96, 123, 97, 83, 87, 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

Author

Tanya Khovanova, Oct 29 2023

Keywords

• nonn
• base
• easy

Comments

a(n) = 0, for n > 10.

Examples

			a(1)=3 because all three 1-digit squares, 1, 4, and 9, have trivially distinct digits.
a(2)=6 because all six 2-digit squares, 16, 25, 36, 49, 64, and 81, have distinct digits.
158407396 = 12586^2: has 9 distinct digits. Thus, this number contributes to a(9). On the other hand, 158382225 = 12585^2 has repeated digits. Thus, it doesn't contribute.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000290, A045540, A049415, A073532, A078255.

Programs

Mathematica

Table[Length[Select[Range[100000], Length[Union[IntegerDigits[#^2]]] == k &&  Length[IntegerDigits[#^2]] == k &]], {k, 10}]

Python

from math import isqrt
from itertools import permutations
def sqr(n): return isqrt(n)**2 == n
def a(n):
    if n > 10: return 0
    return sum(1 for p in permutations("0123456789", n) if p[0] != '0' and sqr(int("".join(p))))
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Oct 29 2023