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

Author

Rémy Sigrist, Jan 03 2018

Keywords

• nonn
• base

Comments

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.

Examples

			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
		

Links

• 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))

Crossrefs

Cf. A076990, A297879.

Programs

PARI

See Links section.