login
Squares whose digits are all even.
11

%I #32 Jan 24 2023 14:25:49

%S 0,4,64,400,484,4624,6084,6400,8464,26244,28224,40000,40804,48400,

%T 68644,88804,228484,242064,248004,446224,462400,608400,640000,806404,

%U 824464,846400,868624,2022084,2226064,2244004,2624400,2822400,2862864,4000000,4008004,4080400

%N Squares whose digits are all even.

%C 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

%H Michael S. Branicky, <a href="/A030098/b030098.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)

%F a(n) = A030097(n)^2. - _Michel Marcus_, Apr 03 2014

%t 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 *)

%t Select[Range[0,3000]^2,AllTrue[IntegerDigits[#],EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 19 2016 *)

%o (Python)

%o from math import isqrt

%o def ok(sq): return all(d in "02468" for d in str(sq))

%o def aupto(limit):

%o sqs = (i*i for i in range(0, isqrt(limit)+1, 2))

%o return list(filter(ok, sqs))

%o print(aupto(4080400)) # _Michael S. Branicky_, May 20 2021

%Y Subsequence of A075787.

%Y Cf. A016754, A030097.

%K nonn,base

%O 1,2

%A _Patrick De Geest_