A397726 a(0) = 0; for k = 0, 1, ..., append a(k) + r^2 and a(k) + s^2 with 0 < r < s as small as possible so as to avoid duplicates.

0, 1, 4, 2, 5, 8, 13, 3, 6, 9, 14, 12, 17, 22, 29, 7, 19, 10, 15, 18, 25, 23, 30, 16, 21, 26, 33, 31, 38, 45, 54, 11, 32, 20, 28, 35, 46, 24, 40, 27, 34, 41, 50, 39, 48, 55, 66, 52, 65, 37, 57, 42, 51, 49, 58, 47, 56, 63, 74, 61, 70, 79, 90, 36, 60, 68, 81, 69

Offset

0,3

Comments

Using powers of 2 instead of squares yields A081241 prefixed by 0.

Using Fibonacci numbers instead of squares yields A095903 prefixed by 0.

A permutation of the nonnegative integers: all terms are distinct; the sequence contains 0; if all the values up to v >= 0 have appeared, v+1 necessarily appears, at the latest, as the first child of v.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, arranged as a binary tree, are:
             ________0________
            |                 |
        ____1___          ____4___
       |        |        |        |
     __2_     __5_     __8_     _13_
    |    |   |    |   |    |   |    |
    3    6   9   14  12   17  22   29

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A081241, A095903, A397727 (inverse), A397728.

Sequence in context: A112962 A226457 A349244 * A277390 A200608 A163358

Adjacent sequences: A397719 A397720 A397723 * A397727 A397728 A397729

Keyword

nonn,tabf,new

Author

Rémy Sigrist, Jul 07 2026

Status

approved