cp's OEIS Frontend

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

%I A029471 #44 Jan 14 2025 11:09:41
%S A029471 1,85,145,245,1189,356717,19590671,35741759,791822369,25313027035
%N A029471 Numbers k that divide the (left) concatenation of all numbers <= k written in base 2 (most significant digit on left).
%C A029471 No other terms below 3*10^10.
%H A029471 <a href="/index/N#concat">Index entries for related sequences</a>
%t A029471 b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* _Robert Price_, Mar 12 2020 *)
%o A029471 (Python)
%o A029471 from itertools import count
%o A029471 def a029471():
%o A029471     total = 0
%o A029471     power_of_two = 1
%o A029471     index_of_two = 0
%o A029471     length_of_string = 0
%o A029471     for n in count(1):
%o A029471         total += (n<<length_of_string)
%o A029471         if n == power_of_two:
%o A029471             power_of_two *= 2
%o A029471             index_of_two += 1
%o A029471         length_of_string += index_of_two
%o A029471         if total % n == 0:
%o A029471             yield n
%o A029471 # _Christian Perfect_, Feb 07 2014
%o A029471 (Python)
%o A029471 def concat_mod(base, k, mod): ...  # See A029479
%o A029471 for k in range(1, 3*10**10):
%o A029471   if concat_mod(2, k, k) == 0: print(k) # _Jason Yuen_, Mar 24 2024
%Y A029471 Cf. A007088.
%Y A029471 Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.
%K A029471 nonn,base,hard,more
%O A029471 1,2
%A A029471 _Olivier Gérard_
%E A029471 One more term from Larry Reeves (larryr(AT)acm.org), Dec 03 2001
%E A029471 Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
%E A029471 a(7)-a(8) from _Max Alekseyev_, May 12 2011
%E A029471 a(9)-a(10) from _Jason Yuen_, Mar 24 2024