A343728 Numbers with all digits even whose squares have all but one digit odd.

0, 2, 4, 6, 24, 44, 86, 244, 424, 444, 846, 2444, 4424, 6286, 42424, 44244, 240244, 244086, 244866, 268286, 420846, 442244, 446286, 628646, 880646, 2402444, 4402044, 4442244, 8448666, 24040244, 24064866, 26682086, 26682866, 26828666, 28244244, 42400424

Offset

1,2

Comments

Of course, the one even digit in the square is always the last digit.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..100

Example

244086 is a term: all its digits are even, and 244086^2 = 59577975396 has all but one digit odd.
244044086 is a term: all its digits are even, and 244044086^2 = 59557515911575396 has all but one digit odd.

Mathematica

Select[Range[0, 10^6], AllTrue[IntegerDigits[#], EvenQ] && AllTrue[Most @ IntegerDigits[#^2], OddQ] &] (* Amiram Eldar, May 20 2021 *)

Prog

(Python)
def ok(n):
  r, s = str(n), str(n*n)
  return all(d in "02468" for d in r) and all(d in "13579" for d in s[:-1])
print(list(filter(ok, range(0, 42400425, 2)))) # Michael S. Branicky, May 20 2021
(Python)
from gmpy2 import digits
A343728_list = [n for n in (2*int(digits(d, 5)) for d in range(10**6)) if set(str(n**2)[:-1]) <= set('13579')] # Chai Wah Wu, May 21 2021

Crossrefs

Cf. A014263, A030098, A343727.

Sequence in context: A141526 A370418 A226169 * A261746 A319575 A318609

Adjacent sequences: A343725 A343726 A343727 * A343729 A343730 A343731

Keyword

nonn,base

Author

Jon E. Schoenfield, May 20 2021

Status

approved