cp's OEIS Frontend

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.

%I A387058 #7 Aug 18 2025 16:16:20
%S A387058 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,
%T A387058 22,27,23,26,24,25,32,49,33,48,34,47,35,46,36,37,44,38,43,39,42,40,41,
%U A387058 45,55,50,71,51,70,52,69,53,68,54,67,56,65,57,64,58,63,59
%N 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.
%C A387058 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.
%H A387058 Rémy Sigrist, <a href="/A387058/b387058.txt">Table of n, a(n) for n = 0..10000</a>
%H A387058 Rémy Sigrist, <a href="/A387058/a387058.gp.txt">PARI program</a>
%H A387058 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A387058 The first terms and corresponding square numbers are:
%e A387058   n   a(n)  Squares
%e A387058   --  ----  -----------------------------
%e A387058    0     0  a(0) = 0^2
%e A387058    1     1  a(0) + a(1) = 1^2, a(1) = 1^2
%e A387058    2     2  a(2) + a(3) = 3^2
%e A387058    3     7  a(2) + a(3) = 3^2
%e A387058    4     3  a(4) + a(5) = 3^2
%e A387058    5     6  a(4) + a(5) = 3^2
%e A387058    6     4  a(6) = 2^2, a(6) + a(7) = 3^2
%e A387058    7     5  a(6) + a(7) = 3^2
%e A387058    8     8  a(8) + a(9) = 5^2
%e A387058    9    17  a(8) + a(9) = 5^2
%e A387058   10     9  a(10) = 3^2
%e A387058   11    10  a(11) + a(12) = 5^2
%e A387058   12    15  a(11) + a(12) = 5^2
%e A387058   13    11  a(13) + a(14) = 5^2
%e A387058   14    14  a(13) + a(14) = 5^2
%e A387058   15    12  a(15) + a(16) = 5^2
%e A387058   16    13  a(15) + a(16) = 5^2
%e A387058   17    16  a(17) = 4^2
%o A387058 (PARI) \\ See Links section.
%Y A387058 Cf. A034175, A387059 (inverse).
%K A387058 nonn
%O A387058 0,3
%A A387058 _Rémy Sigrist_, Aug 15 2025