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

1,1

Comments

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

Links

Table of n, a(n) for n=1..70.

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A104448 A352864 A062466 * A053564 A264236 A216999

Adjacent sequences: A366937 A366938 A366939 * A366941 A366942 A366943

Keyword

nonn,base,easy

Author

Tanya Khovanova, Oct 29 2023

Status

approved