A330717 a(n) is the greatest binary palindrome of the form floor(n/2^k) with k >= 0.

0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 7, 15, 1, 17, 9, 9, 5, 21, 5, 5, 3, 3, 3, 27, 7, 7, 15, 31, 1, 33, 17, 17, 9, 9, 9, 9, 5, 5, 21, 21, 5, 45, 5, 5, 3, 3, 3, 51, 3, 3, 27, 27, 7, 7, 7, 7, 15, 15, 31, 63, 1, 65, 33, 33, 17, 17, 17, 17, 9, 73, 9, 9, 9, 9

Offset: 0

Author

Rémy Sigrist, Dec 28 2019

Keywords

• nonn
• base
• easy

Comments

In other words, a(n) is the greatest binary palindromic prefix of n.

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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A006995, A215467.

Programs

PARI

a(n,b=2) = { my (d=digits(n,b)); forstep (w=#d, 1, -1, my (h=d[1..w]); if (h==Vecrev(h), return (fromdigits(h, b)))); return (0) }

Formula

A070939(a(n)) = A215467(n).

a(n) = 1 iff n is a power of 2.

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

a(a(n)) = a(n).

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