login
A328838
Numbers such that in the primorial base expansion of their squares only even digits appear.
2
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
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)));
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Oct 30 2019
STATUS
approved