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
Examples
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.
Programs
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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
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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
Formula
a(n) <= n^(n+1) - 1. - Bert Dobbelaere, Apr 20 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
Comments