A376814 - OEIS

%I #37 Oct 31 2024 10:41:07

%S 2,2,7,7,21,42,71,268,611,1352,3099,8471,23877,63564,182771,527001,

%T 1671752,5055853

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

%e 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.

%p f:= proc(b) local k,t,F;

%p  t:= 0;

%p  for k from 0 to floor(sqrt(b^b-1)) do

%p    F:= convert(k^2, base, b);

%p    if nops(F) = nops(convert(F,set)) then t:= t+1 fi;

%p  od;

%p  t

%p end proc:

%p map(f, [$2..12]);

%o (Python)

%o from math import isqrt

%o from sympy.ntheory import digits

%o 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

%Y Cf. A119509, A376897.

%K nonn,base,more

%O 2,1

%A _Robert Israel_, Oct 09 2024

%E a(15)-a(16) from _Michael S. Branicky_, Oct 09 2024

%E a(17) from _Michael S. Branicky_, Oct 10 2024

%E a(18) from _Michael S. Branicky_, Oct 14 2024

%E a(19) from _Michael S. Branicky_, Oct 31 2024