A342260 - OEIS

%I #37 Jul 10 2021 11:52:01

%S 3,31,217,268,8399,29110,711243,4676815,31622764,376863606,

%T 12638826343,38121744938,1511790122972,8648472039419,243625577528103

%N a(n)^2 is the least square that, when written in base n, has exactly n digits n-1.

%C 17^(25/2) < a(17) <= 4159201115231103. - _Martin Ehrenstein_, Jul 10 2021

%F a(n) <= n^(n+1) - 1. - _Bert Dobbelaere_, Apr 20 2021

%e a(2) = 3: 3^2 = 9 is the least square with 2 binary ones: 1001;

%e a(3) = 31: 31^2 = 961 is the least square with 3 ternary digits 2: 1022121;

%e a(4) = 217: 217^2 = 47089 = 23133301_4;

%e a(5) = 268: 268^2 = 71824 = 4244244_5.

%o (PARI) isok(k, n) = #select(x->(x==n-1), digits(k^2, n)) == n;

%o a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Apr 05 2021

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def A342260(n):

%o     k = 1

%o     while digits(k**2,n).count(n-1) != n:

%o         k += 1

%o     return k # _Chai Wah Wu_, Apr 05 2021

%Y Cf. A179895, A342545, A342546.

%K nonn,base,more

%O 2,1

%A _Hugo Pfoertner_, Apr 04 2021

%E a(14) from _Martin Ehrenstein_, Apr 17 2021

%E a(15) from _Bert Dobbelaere_, Apr 20 2021

%E a(16) from _Martin Ehrenstein_, Apr 21 2021