A376897 -id:A376897 - cp's OEIS frontend

A376814 a(n) is the number of squares that have all digits distinct in base n.

2, 2, 7, 7, 21, 42, 71, 268, 611, 1352, 3099, 8471, 23877, 63564, 182771, 527001, 1671752, 5055853

Offset: 2

Robert Israel, Oct 09 2024

			a(4) = 7 because the only squares with distinct digits in base 4 are 0^2 = 0_4, 1^2 = 1_4, 2^2 = 10_4, 3^2 = 21_4, 6^2 = 210_4, 7^2 = 301_4 and 15^2 = 3201_4.

Cf. A119509, A376897.

f:= proc(b) local k,t,F;
 t:= 0;
 for k from 0 to floor(sqrt(b^b-1)) do
   F:= convert(k^2, base, b);
   if nops(F) = nops(convert(F,set)) then t:= t+1 fi;
 od;
 t
end proc:
map(f, [$2..12]);

from math import isqrt
from sympy.ntheory import digits
def A376814(n): return sum(1 for k in range(isqrt(n**n-1)+1) if len(s:=digits(k**2,n)[1:])==len(set(s))) # Chai Wah Wu, Oct 09 2024

a(15)-a(16) from Michael S. Branicky, Oct 09 2024
a(17) from Michael S. Branicky, Oct 10 2024
a(18) from Michael S. Branicky, Oct 14 2024
a(19) from Michael S. Branicky, Oct 31 2024

A376898 Positive numbers k such that all the digits in the octal expansion of k^3 are distinct.

Original entry on oeis.org

1, 2, 5, 7, 10, 11, 14, 15, 22, 30, 37, 41, 49, 61, 74, 98, 122

Offset: 1

Kalle Siukola, Oct 08 2024

There are no terms >= 2^8 because 2^24-1 is the largest eight-digit octal number.

			11 is a term because 11^3 = 1331 = 2463_8 in octal and no octal digit occurs more than once.

Cf. A007094, A129525, A376897.

Select[Range[2^8],Length[IntegerDigits[#^3,8]]==Length[Union[IntegerDigits[#^3,8]]]&] (* James C. McMahon, Oct 16 2024 *)

for k in range(1, 2**8):
    octal = format(k**3, "o")
    if len(octal) == len(set(octal)): print(k, end=",")

cp's OEIS Frontend

A376814 a(n) is the number of squares that have all digits distinct in base n.

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