A297879 -id:A297879 - cp's OEIS frontend

A297706 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) XOR a(n+1) XOR a(n+2) is prime (where XOR denotes the bitwise XOR operator).

1, 2, 4, 3, 5, 11, 9, 7, 12, 6, 8, 13, 14, 16, 15, 18, 10, 19, 20, 22, 17, 24, 26, 21, 28, 30, 29, 38, 36, 31, 40, 32, 23, 42, 34, 25, 44, 48, 27, 41, 33, 35, 39, 43, 37, 51, 45, 49, 53, 47, 63, 57, 59, 55, 67, 61, 69, 77, 65, 75, 73, 81, 87, 79, 91, 71, 83

Offset: 1

Rémy Sigrist, Jan 03 2018

See A297879 for the corresponding prime numbers.
This sequence has connections with A076990: here we combine triples of successive terms with the XOR operator, there with the usual addition operator.
The sequence alternates long runs of odd terms and long runs with periodic parity (even, even, odd); changes from one type of run to the other occur near terms such that a(n) XOR a(n+1) XOR a(n+2) = 2; see illustration in Links section.

			The first terms of the sequence are:
    n     a(n)      a(n) XOR a(n+1) XOR a(n+2)
  --    ----      --------------------------
   1       1       7
   2       2       5
   3       4       2
   4       3      13
   5       5       7
   6      11       5
   7       9       2
   8       7      13
   9      12       2
  10       6       3
  11       8      11
  12      13      19
  13      14      17
  14      16      13
  15      15      23
  16      18      11
  17      10      13
  18      19      17
  19      20      19
  20      22      31

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A297706
Rémy Sigrist, Colored scatterplot of the first 25000 terms (where the color is function of the parity of a(n))

Cf. A076990, A297879.

PARI
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See Links section.
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cp's OEIS Frontend

A297706 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) XOR a(n+1) XOR a(n+2) is prime (where XOR denotes the bitwise XOR operator).

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