login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..10.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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