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

0,4

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