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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A096854 A013191 A332959

Adjacent sequences:  A330938 A330939 A330940 * A330942 A330943 A330944

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 04 2020

STATUS

approved

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)