A300890 -id:A300890 - cp's OEIS frontend

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

Rémy Sigrist, Mar 14 2018

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.

			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

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

Cf. A003714, A266191, A300890.

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A307591 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, A000196(2*a(n) + a(n+1)) is a Fibbinary number (A003714).

Original entry on oeis.org

1, 2, 3, 10, 4, 8, 5, 6, 7, 9, 11, 12, 40, 13, 38, 14, 36, 15, 34, 16, 32, 17, 30, 18, 28, 19, 26, 20, 24, 21, 22, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 174, 52, 152, 42, 172, 56, 144, 43, 170, 60, 136, 44, 168, 64, 128, 45, 166, 68, 120, 46, 164, 72, 112

Offset: 1

Rémy Sigrist, Apr 19 2019

This sequence is a variant of A300890 and has interesting graphical features.

Rémy Sigrist, Table of n, a(n) for n = 1..10000 (amended by _Georg Fischer_, May 05 2019)
Rémy Sigrist, Scatterplot of the first 150000 terms

Cf. A000196, A003714, A300890.

s=0; v=1; for (n=1, 64, print1 (v ", "); s+=2^v; for (o=1, oo, if (!bittest(s, o), f=sqrtint(2*v+o); if (bitand(f, 2*f)==0, v=o; break))))

cp's OEIS Frontend

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).

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