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

0,2

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 A330940

Index entries for sequences related to binary expansion of n

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).

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A330941 for the maximum variant.

Cf. A007582, A024036, A191755, A193020.

Sequence in context: A186575 A356318 A233312 * A351010 A020330 A023861

Adjacent sequences: A330937 A330938 A330939 * A330941 A330942 A330943

Keyword

nonn,base

Author

Rémy Sigrist, Jan 04 2020

Status

approved