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

Author

Patrick De Geest

Keywords

• nonn
• base

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)

Crossrefs

Subsequence of A075787.

Cf. A016754, A030097.

Programs

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 *)

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

Formula

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