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A349460 Squares composed of digits {0,2,4}. 1
0, 4, 400, 40000, 2244004, 4000000, 42224004, 224400400, 400000000, 424442404, 4222400400, 22200404004, 22440040000, 40000000000, 42444240400, 422240040000, 2220040400400, 2244004000000, 4000000000000, 4024044024004, 4244424040000, 40244204444224, 42224004000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)

LINKS

Table of n, a(n) for n=1..23.

MATHEMATICA

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

PROG

(C#)

for(ulong num = 0; num < 10000000; num++)

{

ulong sq = num * num;

string sq1 = sq + "";

bool p = true;

string un = "1356789";

for(int a = 0; a < un.Length; a++)

{

if(sq1.Contains(un[a]))

{

p = false;

}

}

if(p)

{

Console.Write(sq1 + ", ");

}

}

Console.WriteLine("done");

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

CROSSREFS

Subsequence of A000290 and A030098.

Sequence in context: A115049 A307929 A202172 * A158111 A259049 A280791

Adjacent sequences: A349457 A349458 A349459 * A349461 A349462 A349463

KEYWORD

nonn,base

AUTHOR

Daniel Blam, Nov 18 2021

STATUS

approved

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Last modified February 8 06:05 EST 2023. Contains 360134 sequences. (Running on oeis4.)