This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328838 #11 Mar 06 2024 01:01:39
%S A328838 0,2,4,8,12,14,22,30,32,38,42,46,48,68,72,74,78,82,118,120,122,136,
%T A328838 138,142,152,154,158,168,172,248,256,258,266,272,282,284,292,298,300,
%U A328838 348,362,368,374,432,442,452,458,492,510,514,548,558,562,574,608,616,652,660,698,704,708,1018,1020,1042,1054,1080,1082,1096,1124
%N A328838 Numbers such that in the primorial base expansion of their squares only even digits appear.
%H A328838 Antti Karttunen, <a href="/A328838/b328838.txt">Table of n, a(n) for n = 1..19309</a>
%H A328838 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A328838 a(n) = A000196(A328850(n)).
%e A328838 For n = 4, its square 16 is written as "220" in primorial base (A049345), as 2*A002110(2) + 2*A002110(1) + 0*A002110(0) = 2*6 + 2*2 = 16, thus 4 is included in this sequence.
%t A328838 q[n_] := Module[{k = n^2, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; AllTrue[s, EvenQ]]; Select[Range[0, 1200], q] (* _Amiram Eldar_, Mar 06 2024 *)
%o A328838 (PARI)
%o A328838 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328838 isA328838(n) = (issquare(A276086(n*n)));
%Y A328838 Cf. A000196, A002110, A010052, A049345, A276086, A328849, A328850.
%K A328838 nonn,base
%O A328838 1,2
%A A328838 _Antti Karttunen_, Oct 30 2019