login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A331804 a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and its reversal (A030101(n)). 1
0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 5, 7, 15, 1, 17, 9, 9, 5, 21, 6, 7, 3, 9, 5, 27, 7, 7, 15, 31, 1, 33, 17, 17, 9, 9, 9, 9, 5, 9, 21, 21, 6, 45, 14, 15, 3, 17, 9, 51, 5, 21, 27, 27, 7, 9, 7, 27, 15, 15, 31, 63, 1, 65, 33, 33, 17, 17, 17, 17, 9, 73, 10, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

We set a(0) = 0 by convention.

a(7479) = 29 ("11101" in binary) is the first term that does not belong to A057890.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192

FORMULA

a(n) = A175466(n, A030101(n)) for any n > 0.

a(n) <= n with equality iff n is a binary palindrome (A006995).

EXAMPLE

The first terms, alongside the binary representations of n and of a(n), are:

  n   a(n)  bin(n)  bin(a(n))

  --  ----  ------  ---------

   0     0       0          0

   1     1       1          1

   2     1      10          1

   3     3      11         11

   4     1     100          1

   5     5     101        101

   6     3     110         11

   7     7     111        111

   8     1    1000          1

   9     9    1001       1001

  10     5    1010        101

  11     5    1011        101

  12     3    1100         11

PROG

(PARI) sub(n) = { my (b=binary(n), s=[0]); for (i=1, #b, if (b[i], for (j=i, #b, s=setunion(s, Set(fromdigits(b[i..j], 2)))))); return (s) }

a(n) = my (i=setintersect(sub(n), sub(fromdigits(Vecrev(binary(n)), 2)))); i[#i]

CROSSREFS

Cf. A006995, A030101, A047813, A057890, A175466.

Sequence in context: A330717 A036233 A145799 * A244568 A331471 A325401

Adjacent sequences:  A331801 A331802 A331803 * A331805 A331806 A331807

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 26 2020

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 January 27 06:18 EST 2022. Contains 350601 sequences. (Running on oeis4.)