A328849 Numbers in whose primorial base expansion only even digits appear.

0, 4, 12, 16, 24, 28, 60, 64, 72, 76, 84, 88, 120, 124, 132, 136, 144, 148, 180, 184, 192, 196, 204, 208, 420, 424, 432, 436, 444, 448, 480, 484, 492, 496, 504, 508, 540, 544, 552, 556, 564, 568, 600, 604, 612, 616, 624, 628, 840, 844, 852, 856, 864, 868, 900, 904, 912, 916, 924, 928, 960, 964, 972, 976, 984, 988, 1020, 1024

Offset: 1

Author

Antti Karttunen, Oct 30 2019

Keywords

• nonn
• base

Comments

Numbers for which the prime factor form (A276086) of their primorial base expansion is a square, A000290.

Examples

			144 is written as "4400" in primorial base (A049345), because 4*A002110(3) + 4*A002110(2) + 0*A002110(1) + 0*A002110(0) = 4*30 + 4*6 = 144, thus all the digits are even and 144 is included in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..9072
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..90720
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A000290, A002110, A010052, A049345, A276086, A276156, A328770.

Cf. A328834, A328850 (squares in this sequence).

Similar sequences: A005823 (ternary), A014263 (decimal), A062880 (quaternary), A351893 (factorial base).

Programs

Mathematica

With[{max = 5}, bases = Prime@ Range[max, 1, -1]; nmax = Times @@ bases - 1; prmBaseDigits[n_] := IntegerDigits[n, MixedRadix[bases]]; Select[Range[0, nmax, 2], AllTrue[prmBaseDigits[#], EvenQ] &]] (* Amiram Eldar, May 23 2023 *)

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA328849(n) = issquare(A276086(n));

Formula

a(n) = 2*A328770(n).

A000196(A276086(a(n))) = A276086(a(n)/2) = A328834(n).