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

0,2

Comments

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

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

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).

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     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

Prog

(PARI) See Links section.

Crossrefs

See A330940 for the minimum variant.

Cf. A002001, A024036, A191755, A193020.

Sequence in context: A290593 A005392 A001196 * A361925 A096854 A013191

Adjacent sequences: A330938 A330939 A330940 * A330942 A330943 A330944

Keyword

nonn,base

Author

Rémy Sigrist, Jan 04 2020

Status

approved