A349460 Squares composed of digits {0,2,4}.

0, 4, 400, 40000, 2244004, 4000000, 42224004, 224400400, 400000000, 424442404, 4222400400, 22200404004, 22440040000, 40000000000, 42444240400, 422240040000, 2220040400400, 2244004000000, 4000000000000, 4024044024004, 4244424040000, 40244204444224, 42224004000000

Offset: 1

Author

Daniel Blam, Nov 18 2021

Keywords

• nonn
• base

Comments

From Marius A. Burtea, Nov 18 2021: (Start)

The sequence is infinite because if m > 0 is a term, then 100*m is also a term.

Also, the squares of the numbers 20602, 2006002, 200060002, ..., (2*10^(2*k) + 6*10^k + 2), k >= 2, are 424442404, 4024044024004, 40024004400240004, 400024000440002400004, ... and have only the digits 0, 2 and 4 and are not divisible by 100. (End)

Crossrefs

Subsequence of A000290 and A030098.

Programs

Magma

[n : n in [s*s:s in [1..1500000]]|Set(Intseq(n)) subset {0,2,4}]; // Marius A. Burtea, Nov 18 2021

Mathematica

Select[Range[0, 10^7, 2]^2, AllTrue[IntegerDigits[#], MemberQ[{0, 2, 4}, #1] &] &] (* Amiram Eldar, Nov 18 2021 *)

Python

from itertools import islice, count
def A349460(): return filter(lambda n: set(str(n)) <= {'0','2','4'},(n*n for n in count(0)))
A349460_list = list(islice(A349460(),20)) # Chai Wah Wu, Nov 19 2021