A330940 a(n) is the least value whose binary representation can be obtained by interleaving (or shuffling) two copies of the binary representation of n.

0, 3, 10, 15, 36, 43, 54, 63, 136, 147, 170, 175, 204, 219, 238, 255, 528, 547, 586, 591, 660, 683, 694, 703, 792, 819, 858, 879, 924, 955, 990, 1023, 2080, 2115, 2186, 2191, 2340, 2347, 2358, 2367, 2600, 2643, 2730, 2735, 2764, 2779, 2798, 2815, 3120, 3171

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 representation of n and of a(n), are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     3       1         11
   2    10      10       1010
   3    15      11       1111
   4    36     100     100100
   5    43     101     101011
   6    54     110     110110
   7    63     111     111111
   8   136    1000   10001000
   9   147    1001   10010011
  10   170    1010   10101010
  11   175    1011   10101111
		

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 A330940
• Index entries for sequences related to binary expansion of n

Crossrefs

See A330941 for the maximum variant.

Cf. A007582, A024036, A191755, A193020.

Programs

PARI

See Links section.

Formula

a(2^k) = 2^k*(1+2^(k+1)) = A007582(k+1) for any k >= 0.

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

a(n) <= A330941(n).