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A340406 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) XOR a(n+1) is a prime number as small as possible (where XOR denotes the bitwise XOR operator). 3
0, 2, 1, 3, 6, 4, 7, 5, 14, 12, 15, 13, 8, 10, 9, 11, 26, 24, 27, 25, 28, 30, 29, 31, 20, 22, 21, 23, 18, 16, 19, 17, 52, 54, 53, 55, 50, 48, 51, 49, 58, 56, 59, 57, 60, 62, 61, 63, 46, 44, 47, 45, 40, 42, 41, 43, 32, 34, 33, 35, 38, 36, 39, 37, 102, 100, 103 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence has connections with A003188; their scatterplots are alike.

This sequence appears to be a permutation of the nonnegative integers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Scatterplot of the first 2^16 terms

EXAMPLE

The first terms, alongside a(n) XOR a(n+1), are:

  n   a(n)  a(n) XOR a(n+1)

  --  ----  ---------------

   0     0                2

   1     2                3

   2     1                2

   3     3                5

   4     6                2

   5     4                3

   6     7                2

   7     5               11

   8    14                2

   9    12                3

  10    15                2

  11    13                5

  12     8                2

PROG

(PARI) s=0; v=0; for (n=0, 66, print1 (v", "); s+=2^v; forprime (p=2, oo, if (!bittest(s, w=bitxor(v, p)), v=w; break)))

CROSSREFS

Cf. A003188, A340446 (cube analog), A340447 (Fibonacci analog).

Sequence in context: A133904 A245182 A209160 * A257881 A268182 A094339

Adjacent sequences:  A340403 A340404 A340405 * A340407 A340408 A340409

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 06 2021

STATUS

approved

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Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)