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

1,2

Comments

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

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.

Formula

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

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

Example

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.

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 *)

Prog

(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));

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).

Sequence in context: A310568 A257692 A053006 * A261958 A057962 A186303

Adjacent sequences: A328846 A328847 A328848 * A328850 A328851 A328852

Keyword

nonn,base

Author

Antti Karttunen, Oct 30 2019

Status

approved