A029450 Numbers k that divide the (right) concatenation of all numbers <= k written in base 5 (most significant digit on left).

1, 5, 16, 23, 25, 35, 80, 125, 160, 205, 352, 625, 800, 1120, 1875, 2221, 3125, 6000, 9375, 10000, 11120, 15625, 19184, 21875, 30000, 50000, 55135, 58775, 66800, 71875, 78125, 88000, 88385, 171875, 200000, 390625, 472000, 715189, 734375, 1000000, 1953125, 2050000

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..83

Mathematica

b = 5; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 10 2020 *)

Prog

(PARI) is(k, b=5) = my(c, s, t=1, u); while(t<=k, u=b*t-1; c=min(u, k)-t+1; s=s*Mod(u+1, k)^c+lift((t*u+1)*Mod(u+1, k*u^2)^c-u*(c+t)-1)/u^2; t=u+1); !s; \\ Jinyuan Wang, May 03 2025
(Python)
def ok(k): return concat_mod(5, 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. A007091.

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

Sequence in context: A042603 A031120 A395566 * A225539 A299124 A278415

Adjacent sequences: A029447 A029448 A029449 * A029451 A029452 A029453

Keyword

nonn,base

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

a(40)-a(42) from Jinyuan Wang, May 03 2025

Status

approved