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)).

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

Offset: 0

Author

Rémy Sigrist, Jan 26 2020

Keywords

• nonn
• base

Comments

We set a(0) = 0 by convention.

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

Examples

			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
		

Links

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

Crossrefs

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

Programs

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]

Formula

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

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