A029471 Numbers k that divide the (left) concatenation of all numbers <= k written in base 2 (most significant digit on left).

1, 85, 145, 245, 1189, 356717, 19590671, 35741759, 791822369, 25313027035

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base
• hard
• more

Comments

No other terms below 3*10^10.

Links

• Index entries for related sequences

Crossrefs

Cf. A007088.

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

Programs

Mathematica

b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Python

from itertools import count
def a029471():
    total = 0
    power_of_two = 1
    index_of_two = 0
    length_of_string = 0
    for n in count(1):
        total += (n<Christian Perfect, Feb 07 2014

Python

def concat_mod(base, k, mod): ...  # See A029479
for k in range(1, 3*10**10):
  if concat_mod(2, k, k) == 0: print(k) # Jason Yuen, Mar 24 2024

Extensions

One more term from Larry Reeves (larryr(AT)acm.org), Dec 03 2001

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002

a(7)-a(8) from Max Alekseyev, May 12 2011

a(9)-a(10) from Jason Yuen, Mar 24 2024