A029454 Numbers k that divide the (right) concatenation of all numbers <= k written in base 9 (most significant digit on left).

1, 3, 9, 27, 33, 47, 51, 64, 81, 97, 135, 153, 192, 243, 405, 576, 729, 933, 1152, 2187, 3456, 6561, 9099, 10368, 19683, 27008, 31104, 59049, 72981, 91584, 108864, 111537, 126021, 137781, 139968, 177147, 260253, 326592, 413343, 419904, 438543, 531441, 553797, 626624

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..110

Mathematica

b = 9; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

Prog

(PARI) lista(nn, m=9) = my(t); for(k=1, nn, t=t*m^(1+logint(k, m))+k; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, May 03 2025
(Python)
def ok(k): return concat_mod(9, 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 29 2026

Crossrefs

Cf. A007095.

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

Sequence in context: A111117 A018675 A061972 * A095309 A191126 A161141

Adjacent sequences: A029451 A029452 A029453 * A029455 A029456 A029457

Keyword

nonn,base

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

a(42)-a(44) from Jinyuan Wang, May 03 2025

Status

approved