cp's OEIS Frontend

A338502 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(1) XOR ... XOR a(n) is a square (where XOR denotes the bitwise XOR operator).

%I A338502 #9 Nov 03 2020 03:24:50
%S A338502 0,1,5,4,9,8,17,16,25,24,37,21,33,20,13,45,32,29,40,48,65,36,53,72,61,
%T A338502 52,80,57,93,64,85,49,81,88,56,96,117,100,68,125,105,116,101,120,112,
%U A338502 73,89,137,84,109,141,180,113,133,160,132,161,152,121,144,128
%N A338502 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(1) XOR ... XOR a(n) is a square (where XOR denotes the bitwise XOR operator).
%C A338502 All terms belong to A042948.
%H A338502 Rémy Sigrist, <a href="/A338502/b338502.txt">Table of n, a(n) for n = 1..10000</a>
%H A338502 Rémy Sigrist, <a href="/A338502/a338502.gp.txt">PARI program for A338502</a>
%e A338502 The first terms, alongside a(1) XOR ... XOR a(n), are:
%e A338502   n   a(n)  a(1) AND ... AND a(n)
%e A338502   --  ----  ---------------------
%e A338502    1     0                0 = 0^2
%e A338502    2     1                1 = 1^2
%e A338502    3     5                4 = 2^2
%e A338502    4     4                0 = 0^2
%e A338502    5     9                9 = 3^2
%e A338502    6     8                1 = 1^2
%e A338502    7    17               16 = 4^2
%e A338502    8    16                0 = 0^2
%e A338502    9    25               25 = 5^2
%e A338502   10    24                1 = 1^2
%e A338502   11    37               36 = 6^2
%e A338502   12    21               49 = 7^2
%o A338502 (PARI) See Links section.
%Y A338502 Cf. A042948, A042964, A292388 (prime variant), A338503.
%K A338502 nonn,base
%O A338502 1,3
%A A338502 _Rémy Sigrist_, Oct 31 2020