A342546 a(n)^2 is the least square with exactly n 1's in base n.
3, 7, 73, 141, 1417, 17130, 11677, 187955, 10252371, 20440221, 1550384575, 10645648530, 80224807014, 829050923579, 17071371319785, 599574561430568
Offset: 2
Examples
n a(n) a(n)^2 in base n 2 3 9 1001 3 7 49 1211 4 73 5329 1103101 5 141 19881 1114011 6 1417 2007889 111011441 7 17130 293436900 10162113111 8 11677 136352329 1010111111 9 187955 35327082025 111160121111 10 10252371 105111111121641 105111111121641
Programs
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PARI
for(b=2,10,for(k=1,oo,my(s=k^2,d=digits(s,b));if(sum(k=1,#d,d[k]==1)==b,print1(k,", ");break)))
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Python
from sympy import integer_nthroot from numba import njit @njit # works with 64 bits through a(12) def digits1(n, b): count1 = 0 while n >= b: n, r = divmod(n, b) count1 += (r==1) return count1 + (n==1) def a(n): an = integer_nthroot(n**(n-1), 2)[0] + 1 while digits1(an*an, n) != n: an += 1 return an print([a(n) for n in range(2, 10)]) # Michael S. Branicky, Apr 07 2021
Extensions
a(14) from Chai Wah Wu, Apr 14 2021
a(15)-a(16) from Giovanni Resta, Apr 17 2021
a(17) from Martin Ehrenstein, May 29 2021