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

3, 31, 217, 268, 8399, 29110, 711243, 4676815, 31622764, 376863606, 12638826343, 38121744938, 1511790122972, 8648472039419, 243625577528103

Offset

2,1

Comments

17^(25/2) < a(17) <= 4159201115231103. - Martin Ehrenstein, Jul 10 2021

Links

Table of n, a(n) for n=2..16.

Formula

a(n) <= n^(n+1) - 1. - Bert Dobbelaere, Apr 20 2021

Example

a(2) = 3: 3^2 = 9 is the least square with 2 binary ones: 1001;
a(3) = 31: 31^2 = 961 is the least square with 3 ternary digits 2: 1022121;
a(4) = 217: 217^2 = 47089 = 23133301_4;
a(5) = 268: 268^2 = 71824 = 4244244_5.

Prog

(PARI) isok(k, n) = #select(x->(x==n-1), digits(k^2, n)) == n;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Apr 05 2021
(Python)
from sympy.ntheory.factor_ import digits
def A342260(n):
    k = 1
    while digits(k**2, n).count(n-1) != n:
        k += 1
    return k # Chai Wah Wu, Apr 05 2021

Crossrefs

Cf. A179895, A342545, A342546.

Sequence in context: A203242 A121099 A197746 * A121147 A114654 A198151

Adjacent sequences: A342257 A342258 A342259 * A342261 A342262 A342263

Keyword

nonn,base,more

Author

Hugo Pfoertner, Apr 04 2021

Extensions

a(14) from Martin Ehrenstein, Apr 17 2021

a(15) from Bert Dobbelaere, Apr 20 2021

a(16) from Martin Ehrenstein, Apr 21 2021

Status

approved