A061931 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 2 (most significant digit on right).

1, 3, 7, 39, 63, 523, 4983, 25007, 892217, 1142775, 1381311, 1751751

Offset: 1

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

• nonn
• base
• more

Comments

This sequence differs from A029495 in that all least significant zeros are removed before concatenation.

No more terms < 10^7. [Lars Blomberg, Oct 17 2011]

Examples

			1234567 -> (1)(01)(11)(001)(101)(011)(111) base 2 -> 1111110111111 base 2 = 8127 and 7 divides 8127.
		

Links

• Index entries for related sequences

Crossrefs

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[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 07 2020 *)

Python

def agen():
  k, concat = 1, 1
  while True:
    if concat%k == 0: yield k
    revbink_even = (bin(k+1)[2:])[::-1]
    revbink_odd = '1' + revbink_even[1:]
    add_str = revbink_even[revbink_even.index('1'):] + revbink_odd
    concat = (concat << len(add_str)) + int(add_str, 2)
    k += 2
g = agen()
print([next(g) for i in range(8)]) # Michael S. Branicky, Jan 03 2021

Extensions

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

a(9)-a(12) from Lars Blomberg, Oct 17 2011