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

Author

Robert Israel, Oct 09 2024

Keywords

• nonn
• base
• more

Examples

			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.
		

Crossrefs

Cf. A119509, A376897.

Programs

Maple

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]);

Python

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

Extensions

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