login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300654 a(n) is the greatest k such that, for i = 1..k, the binary representation of i appears as a substring in the binary representation of 1/n (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion). 2
2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 8, 2, 9, 2, 2, 2, 4, 4, 16, 4, 4, 8, 6, 2, 8, 9, 11, 2, 20, 2, 2, 2, 4, 4, 8, 4, 32, 16, 6, 4, 4, 4, 8, 8, 6, 6, 12, 2, 12, 8, 2, 9, 33, 11, 10, 2, 8, 20, 37, 2, 41, 2, 2, 2, 4, 4, 64, 4, 14, 8, 14, 4, 4, 32, 11, 16, 17, 6, 22, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, a(n) is the greatest k such that A300653(n, k) = k.

This sequence has similarities with A144016: here we consider the binary expansion of 1/n, there the binary expansion of n.

LINKS

Table of n, a(n) for n=1..80.

Rémy Sigrist, PARI program for A300654

FORMULA

a(2*n) = a(n).

a(n) = 2 iff n belongs to A300630.

EXAMPLE

For n = 19:

- the binary expansion of 1/19 is 0.0000(110101111001010000) (with repeating digits in parentheses),

- the first occurrence of the binary representation of k for k = 1..16 is:

  k   bin(k)  bin(1/19) with bin(k) in parentheses

  --  ------  ------------------------------------

   1      1   0.0000(1)101...

   2     10   0.00001(10)101...

   3     11   0.0000(11)010...

   4    100   0.000011010111(100)101...

   5    101   0.00001(101)011...

   6    110   0.0000(110)101...

   7    111   0.000011010(111)100...

   8   1000   0.00001101011110010(1000)011...

   9   1001   0.000011010111(1001)010...

  10   1010   0.00001(1010)111...

  11   1011   0.0000110(1011)110...

  12   1100   0.00001101011(1100)101...

  13   1101   0.0000(1101)011...

  14   1110   0.0000110101(1110)010...

  15   1111   0.000011010(1111)001...

  16  10000   0.00001101011110010(10000)110...

- the binary representation of 17 (10001) is missing,

- hence a(19) = 16.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A144016, A300653, A300630.

Sequence in context: A277561 A317684 A127973 * A023157 A228849 A069733

Adjacent sequences:  A300651 A300652 A300653 * A300655 A300656 A300657

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 10 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)