A030098 Squares whose digits are all even.

0, 4, 64, 400, 484, 4624, 6084, 6400, 8464, 26244, 28224, 40000, 40804, 48400, 68644, 88804, 228484, 242064, 248004, 446224, 462400, 608400, 640000, 806404, 824464, 846400, 868624, 2022084, 2226064, 2244004, 2624400, 2822400, 2862864, 4000000, 4008004, 4080400

Offset

1,2

Comments

On the other hand, the only squares whose digits are all odd are 1 and 9, because the tens digit of all odd squares >= 25 (A016754) is always even. - Bernard Schott, Jan 24 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Formula

a(n) = A030097(n)^2. - Michel Marcus, Apr 03 2014

Mathematica

t = {}; n = -1; While[Length[t] < 1000, n++; If[Intersection[IntegerDigits[n^2], {1, 3, 5, 7, 9}] == {}, AppendTo[t, n^2]]] (* T. D. Noe, Apr 03 2014 *)
Select[Range[0, 3000]^2, AllTrue[IntegerDigits[#], EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 19 2016 *)

Prog

(Python)
from math import isqrt
def ok(sq): return all(d in "02468" for d in str(sq))
def aupto(limit):
  sqs = (i*i for i in range(0, isqrt(limit)+1, 2))
  return list(filter(ok, sqs))
print(aupto(4080400)) # Michael S. Branicky, May 20 2021

Crossrefs

Subsequence of A075787.

Cf. A016754, A030097.

Sequence in context: A249483 A165516 A064935 * A087045 A169801 A103751

Adjacent sequences: A030095 A030096 A030097 * A030099 A030100 A030101

Keyword

nonn,base

Author

Patrick De Geest

Status

approved