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

1,2

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.

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))

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A076990, A297879.

Sequence in context: A232799 A276472 A245702 * A374799 A093416 A073944

Adjacent sequences: A297703 A297704 A297705 * A297707 A297708 A297709

Keyword

nonn,base

Author

Rémy Sigrist, Jan 03 2018

Status

approved