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A336797
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Numbers, not divisible by 3, whose squares have exactly 4 nonzero digits in base 3.
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0
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OFFSET
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1,1
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COMMENTS
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Is this sequence infinite?
Next term, if it exists, is > 3^500. - James Rayman, Feb 05 2021
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LINKS
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EXAMPLE
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7^2=49 in base 3 is 1211, so 7 is a term.
14^2=196 in base 3 is 21021, so 14 is a term.
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MATHEMATICA
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Select[Range[4000], Mod[#, 3] > 0 && Length @ Select[IntegerDigits[#^2, 3], #1 > 0 &] == 4 &] (* Amiram Eldar, Jan 27 2021 *)
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PROG
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(PARI) isok(n) = (n%3) && #select(x->x, digits(n^2, 3)) == 4;
(Python)
from gmpy2 import isqrt, is_square
import itertools
N = 1000
powers = [1]
a_list = []
while len(powers) < N: powers.append(3 * powers[-1])
def attempt(n):
if is_square(n): a_list.append(int(isqrt(n)))
for A, B, C in itertools.combinations(powers[1:], 3):
for a, b, c in itertools.product([1, 2], repeat=3):
attempt(a*A + b*B + c*C + 1)
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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STATUS
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approved
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