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A342260 a(n)^2 is the least square that, when written in base n, has exactly n digits n-1.

%I A342260 #37 Jul 10 2021 11:52:01
%S A342260 3,31,217,268,8399,29110,711243,4676815,31622764,376863606,
%T A342260 12638826343,38121744938,1511790122972,8648472039419,243625577528103
%N A342260 a(n)^2 is the least square that, when written in base n, has exactly n digits n-1.
%C A342260 17^(25/2) < a(17) <= 4159201115231103. - _Martin Ehrenstein_, Jul 10 2021
%F A342260 a(n) <= n^(n+1) - 1. - _Bert Dobbelaere_, Apr 20 2021
%e A342260 a(2) = 3: 3^2 = 9 is the least square with 2 binary ones: 1001;
%e A342260 a(3) = 31: 31^2 = 961 is the least square with 3 ternary digits 2: 1022121;
%e A342260 a(4) = 217: 217^2 = 47089 = 23133301_4;
%e A342260 a(5) = 268: 268^2 = 71824 = 4244244_5.
%o A342260 (PARI) isok(k, n) = #select(x->(x==n-1), digits(k^2, n)) == n;
%o A342260 a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Apr 05 2021
%o A342260 (Python)
%o A342260 from sympy.ntheory.factor_ import digits
%o A342260 def A342260(n):
%o A342260     k = 1
%o A342260     while digits(k**2,n).count(n-1) != n:
%o A342260         k += 1
%o A342260     return k # _Chai Wah Wu_, Apr 05 2021
%Y A342260 Cf. A179895, A342545, A342546.
%K A342260 nonn,base,more
%O A342260 2,1
%A A342260 _Hugo Pfoertner_, Apr 04 2021
%E A342260 a(14) from _Martin Ehrenstein_, Apr 17 2021
%E A342260 a(15) from _Bert Dobbelaere_, Apr 20 2021
%E A342260 a(16) from _Martin Ehrenstein_, Apr 21 2021