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A328849 Numbers in whose primorial base expansion only even digits appear. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers for which the prime factor form (A276086) of their primorial base expansion is a square, A000290.
LINKS
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. 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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Oct 30 2019
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)