A340406 - OEIS

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).

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: A245182 A209160 A371418 * A257881 A268182 A094339

Adjacent sequences: A340403 A340404 A340405 * A340407 A340408 A340409

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 06 2021

STATUS

approved