A397728 a(0) = 0, a(1) = 1; for k = 0, 1, ..., append a(k) + p and a(k) + q with 0 < p < q two prime numbers as small as possible so as to avoid duplicates.

0, 1, 2, 3, 4, 6, 5, 7, 8, 10, 9, 11, 13, 17, 12, 16, 14, 18, 15, 19, 21, 23, 20, 22, 24, 28, 26, 30, 34, 36, 25, 29, 27, 33, 31, 37, 35, 41, 32, 38, 42, 48, 40, 44, 46, 52, 39, 43, 45, 51, 47, 53, 57, 59, 49, 55, 61, 67, 63, 65, 73, 77, 54, 56, 58, 60, 50, 64

Offset

0,3

Comments

A permutation of the nonnegative integers: all terms are distinct; if all the values up to v >= 0 with the same parity as v have appeared, v+2 necessarily appears, at the latest, as the first child of v; as the sequence contains 0 (respectively 1), it contains every even numbers (respectively every odd numbers).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10001

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, arranged as two binary trees, are:
         ____0____           ____1____
        |         |         |         |
      __2_      __3_      __4_      __6_
     |    |    |    |    |    |    |    |
     5    7    8   10    9   11   13   17

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A397726, A397729 (inverse).

Sequence in context: A371424 A371425 A361940 * A361926 A397729 A332805

Adjacent sequences: A397723 A397726 A397727 * A397729 A397730 A397731

Keyword

nonn,new

Author

Rémy Sigrist, Jul 08 2026

Status

approved