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

Author

Jon E. Schoenfield, May 20 2021

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A014263, A030098, A343727.

Programs

Mathematica

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

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