A387058 Lexicographically earliest sequence of distinct nonnegative integers such that each term is a square number or belongs to a run of two consecutive terms summing to a square number.

0, 1, 2, 7, 3, 6, 4, 5, 8, 17, 9, 10, 15, 11, 14, 12, 13, 16, 18, 31, 19, 30, 20, 29, 21, 28, 22, 27, 23, 26, 24, 25, 32, 49, 33, 48, 34, 47, 35, 46, 36, 37, 44, 38, 43, 39, 42, 40, 41, 45, 55, 50, 71, 51, 70, 52, 69, 53, 68, 54, 67, 56, 65, 57, 64, 58, 63, 59

Offset: 0

Author

Rémy Sigrist, Aug 15 2025

Keywords

• nonn

Comments

This sequence is a permutation of the nonnegative as each term belongs to a run of one or two terms summing to a square number, and after such a run we can extend the sequence with the least missing value.

Examples

			The first terms and corresponding square numbers are:
  n   a(n)  Squares
  --  ----  -----------------------------
   0     0  a(0) = 0^2
   1     1  a(0) + a(1) = 1^2, a(1) = 1^2
   2     2  a(2) + a(3) = 3^2
   3     7  a(2) + a(3) = 3^2
   4     3  a(4) + a(5) = 3^2
   5     6  a(4) + a(5) = 3^2
   6     4  a(6) = 2^2, a(6) + a(7) = 3^2
   7     5  a(6) + a(7) = 3^2
   8     8  a(8) + a(9) = 5^2
   9    17  a(8) + a(9) = 5^2
  10     9  a(10) = 3^2
  11    10  a(11) + a(12) = 5^2
  12    15  a(11) + a(12) = 5^2
  13    11  a(13) + a(14) = 5^2
  14    14  a(13) + a(14) = 5^2
  15    12  a(15) + a(16) = 5^2
  16    13  a(15) + a(16) = 5^2
  17    16  a(17) = 4^2
		

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

Crossrefs

Cf. A034175, A387059 (inverse).

Programs

PARI

\\ See Links section.