A328838 Numbers such that in the primorial base expansion of their squares only even digits appear.

0, 2, 4, 8, 12, 14, 22, 30, 32, 38, 42, 46, 48, 68, 72, 74, 78, 82, 118, 120, 122, 136, 138, 142, 152, 154, 158, 168, 172, 248, 256, 258, 266, 272, 282, 284, 292, 298, 300, 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

Offset: 1

Author

Antti Karttunen, Oct 30 2019

Keywords

• nonn
• base

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19309
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A000196, A002110, A010052, A049345, A276086, A328849, A328850.

Programs

Mathematica

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 *)

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA328838(n) = (issquare(A276086(n*n)));

Formula

a(n) = A000196(A328850(n)).