A257868 Negative integers n such that in balanced ternary representation the number of occurrences of each trit doubles when n is squared.
-314, -898, -942, -2694, -2824, -2826, -2962, -3014, -3070, -3074, -8066, -8082, -8090, -8096, -8132, -8170, -8224, -8336, -8426, -8434, -8450, -8472, -8478, -8480, -8618, -8656, -8870, -8886, -8918, -9008, -9042, -9210, -9222, -9224, -24198, -24226, -24246
Offset: 1
Examples
-898 is in the sequence because -898 = LL10L1L_bal3 and (-898)^2 = 806404 = 1LLLL00L1LLL11_bal3, where L represents (-1).
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
- Wikipedia, Balanced ternary
Crossrefs
Programs
-
Maple
p:= proc(n) local d, m, r; m:=abs(n); r:=0; while m>0 do d:= irem(m, 3, 'm'); if d=2 then m:=m+1 fi; r:=r+x^`if`(n>0, d, irem(3-d, 3)) od; r end: a:= proc(n) option remember; local k; for k from -1+`if`(n=1, 0, a(n-1)) by -1 while p(k)*2<>p(k^2) do od; k end: seq(a(n), n=1..50); -
Python
def a(n): s=[] l=[] x=0 while n>0: x=n%3 n//=3 if x==2: x=-1 n+=1 s.append(x) l.append(-x) return [s, l] print([-n for n in range(1, 25001) if a(n**2)[0].count(-1)==2*a(n)[1].count(-1) and a(n**2)[0].count(1)==2*a(n)[1].count(1) and a(n**2)[0].count(0)==2*a(n)[1].count(0)]) # Indranil Ghosh, Jun 07 2017