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

Author

Rémy Sigrist, Mar 14 2018

Keywords

• nonn
• base

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.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A300896

Crossrefs

Cf. A003714, A266191, A300890.

Programs

PARI

See Links section.