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

1,2

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]

Links

Table of n, a(n) for n=1..12.

Index entries for related sequences

Example

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

Mathematica

b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[
c = Join[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 07 2020 *)

Prog

(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

Crossrefs

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

Sequence in context: A335812 A282427 A192198 * A057203 A056250 A113870

Adjacent sequences: A061928 A061929 A061930 * A061932 A061933 A061934

Keyword

nonn,base,more

Author

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

Extensions

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

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

Status

approved