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

2,1

Links

Table of n, a(n) for n=2..19.

Example

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.

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]);

Prog

(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

Crossrefs

Cf. A119509, A376897.

Sequence in context: A244049 A271229 A199886 * A117779 A300952 A195326

Adjacent sequences: A376811 A376812 A376813 * A376815 A376816 A376817

Keyword

nonn,base,more

Author

Robert Israel, 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

Status

approved