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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..19309

Index entries for sequences related to primorial base.

Formula

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

Example

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.

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 *)

Prog

(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)));

Crossrefs

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

Sequence in context: A024911 A024906 A160162 * A064711 A050865 A354109

Adjacent sequences: A328835 A328836 A328837 * A328839 A328840 A328841

Keyword

nonn,base

Author

Antti Karttunen, Oct 30 2019

Status

approved