A330941 a(n) is the greatest value whose binary representation can be obtained by interleaving (or shuffling) two copies of the binary representation of n.

0, 3, 12, 15, 48, 53, 60, 63, 192, 201, 212, 219, 240, 245, 252, 255, 768, 785, 804, 819, 848, 853, 876, 887, 960, 969, 980, 987, 1008, 1013, 1020, 1023, 3072, 3105, 3140, 3171, 3216, 3237, 3276, 3303, 3392, 3401, 3412, 3435, 3504, 3509, 3548, 3567, 3840, 3857

Offset: 0

Author

Rémy Sigrist, Jan 04 2020

Keywords

• nonn
• base

Comments

The binary representation of all positive terms are square binary words (see A191755).

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     3       1          11
   2    12      10        1100
   3    15      11        1111
   4    48     100      110000
   5    53     101      110101
   6    60     110      111100
   7    63     111      111111
   8   192    1000    11000000
   9   201    1001    11001001
  10   212    1010    11010100
  11   219    1011    11011011
  12   240    1100    11110000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Logarithmic scatterplot of the first difference of the first 2^13 terms
• Rémy Sigrist, PARI program for A330941
• Index entries for sequences related to binary expansion of n

Crossrefs

See A330940 for the minimum variant.

Cf. A002001, A024036, A191755, A193020.

Programs

PARI

See Links section.

Formula

a(2^k) = 3*4^k = A002001(k+1) for any k >= 0.

a(2^k-1) = 4^k-1 = A024036(k) for any k >= 0.

a(n) >= A330940(n).