A029448 Numbers k that divide the (right) concatenation of all numbers <= k written in base 3 (most significant digit on left).

1, 3, 4, 9, 12, 27, 72, 81, 104, 216, 219, 243, 324, 729, 756, 972, 2187, 3888, 3921, 6561, 9477, 11664, 16848, 19683, 21156, 22599, 26244, 26811, 29245, 30132, 32805, 37665, 38788, 39852, 40905, 45756, 46965, 47871, 59049, 78732, 80676, 82380, 90396, 91740, 92340

Offset

1,2

Comments

Includes all powers of 3. - Robert Israel, Nov 06 2025

Links

Michael S. Branicky, Table of n, a(n) for n = 1..125 (terms 1..79 from Jianing Song; terms 1..71 from Robert Israel)

Maple

c:= 1: R:= 1: count:= 1:
for k from 2 while count < 50 do
  c:= c * 3^(1+ilog[3](k)) + k;
  if c mod k = 0 then R:= R, k; count:= count+1 fi
od;
R; # Robert Israel, Nov 06 2025

Mathematica

b = 3; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 10 2020 *)

Prog

(PARI) c=0; for(d=1, 3^15, for(n=d, -1+d*=3, (c=c*d+n)%n || print1(n", ")); d--) \\ Jianing Song, Apr 26 2026, copied from M. F. Hasler's program in A029455
(Python)
def ok(k): return concat_mod(3, k, k) == 0   # uses concat_mod by Jason Yuen in A029455
print([k for k in range(1, 10**5) if ok(k)]) # Michael S. Branicky, Apr 26 2026

Crossrefs

Cf. A007089.

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Sequence in context: A353306 A211221 A376684 * A249179 A103014 A116552

Adjacent sequences: A029445 A029446 A029447 * A029449 A029450 A029451

Keyword

nonn,base

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

Status

approved