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 A336797 Numbers, not divisible by 3, whose squares have exactly 4 nonzero digits in base 3. 0
 7, 14, 16, 17, 26, 35, 47, 68, 350, 3788 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Is this sequence infinite? Next term, if it exists, is > 3^500. - James Rayman, Feb 05 2021 LINKS Alessio Moscariello, On sparse perfect powers, arXiv:2101.10415 [math.NT], 2021. See Question 11 p. 9. EXAMPLE 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. MATHEMATICA Select[Range[4000], Mod[#, 3] > 0 && Length @ Select[IntegerDigits[#^2, 3], #1 > 0 &] == 4 &] (* Amiram Eldar, Jan 27 2021 *) PROG (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) print(sorted(a_list)) # James Rayman, Feb 05 2021 CROSSREFS Cf. A007089 (numbers in base 3), A160385. Sequence in context: A086779 A269173 A167197 * A100599 A198390 A118905 Adjacent sequences:  A336794 A336795 A336796 * A336798 A336799 A336800 KEYWORD nonn,base,more AUTHOR Michel Marcus, Jan 27 2021 STATUS approved

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Last modified May 16 10:20 EDT 2021. Contains 343940 sequences. (Running on oeis4.)