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a(n)^2 is the least square with exactly n 1's in base n.
2

%I #28 May 30 2021 12:59:47

%S 3,7,73,141,1417,17130,11677,187955,10252371,20440221,1550384575,

%T 10645648530,80224807014,829050923579,17071371319785,599574561430568

%N a(n)^2 is the least square with exactly n 1's in base n.

%e n a(n) a(n)^2 in base n

%e 2 3 9 1001

%e 3 7 49 1211

%e 4 73 5329 1103101

%e 5 141 19881 1114011

%e 6 1417 2007889 111011441

%e 7 17130 293436900 10162113111

%e 8 11677 136352329 1010111111

%e 9 187955 35327082025 111160121111

%e 10 10252371 105111111121641 105111111121641

%o (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)))

%o (Python)

%o from sympy import integer_nthroot

%o from numba import njit

%o @njit # works with 64 bits through a(12)

%o def digits1(n, b):

%o count1 = 0

%o while n >= b:

%o n, r = divmod(n, b)

%o count1 += (r==1)

%o return count1 + (n==1)

%o def a(n):

%o an = integer_nthroot(n**(n-1), 2)[0] + 1

%o while digits1(an*an, n) != n: an += 1

%o return an

%o print([a(n) for n in range(2, 10)]) # _Michael S. Branicky_, Apr 07 2021

%Y Cf. A000290, A342260, A342545.

%K nonn,base,more

%O 2,1

%A _Hugo Pfoertner_, Apr 07 2021

%E a(14) from _Chai Wah Wu_, Apr 14 2021

%E a(15)-a(16) from _Giovanni Resta_, Apr 17 2021

%E a(17) from _Martin Ehrenstein_, May 29 2021