A300896 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) + a(n+1) + a(n+2) is a Fibbinary number (A003714).

1, 2, 5, 3, 8, 6, 4, 7, 9, 16, 11, 10, 12, 14, 15, 13, 36, 17, 19, 28, 18, 20, 26, 22, 21, 23, 24, 25, 31, 29, 68, 32, 30, 66, 33, 34, 61, 35, 37, 56, 39, 38, 51, 40, 41, 47, 42, 43, 44, 45, 48, 52, 46, 50, 49, 62, 27, 55, 54, 53, 57, 58, 141, 59, 60, 137, 63

Offset

1,2

Comments

This sequence has similarities with A266191: here we consider the sum of triples of consecutive terms, there their product.

This sequence is conjectured to be a permutation of the natural numbers.

See A300890 for a similar sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A300896

Example

The first terms, alongside the binary representation of triples of consecutive terms, are:
  n   a(n)    binary(a(n) + a(n+1) + a(n+2))
  --  ----    ------------------------------
   1     1       1000
   2     2       1010
   3     5      10000
   4     3      10001
   5     8      10010
   6     6      10001
   7     4      10100
   8     7     100000
   9     9     100100
  10    16     100101
  11    11     100001
  12    10     100100
  13    12     101001
  14    14     101010
  15    15    1000000
  16    13    1000010
  17    36    1001000
  18    17    1000000
  19    19    1000001
  20    28    1000010

Prog

(PARI) See Links section.

Crossrefs

Cf. A003714, A266191, A300890.

Sequence in context: A063955 A097594 A204980 * A191732 A197393 A257271

Adjacent sequences: A300893 A300894 A300895 * A300897 A300898 A300899

Keyword

nonn,base

Author

Rémy Sigrist, Mar 14 2018

Status

approved