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A298816 a(n) is the binary XOR of all n-bit squares, with a(2)=0 indicating that no 2-bit squares exist.

%I A298816 #12 Mar 01 2025 22:49:41
%S A298816 1,0,4,9,9,21,12,28,449,577,357,997,6085,14533,12517,15077,121125,
%T A298816 152869,400028,1041052,1290704,2556368,4913664,11950592,22421376,
%U A298816 63692672,7674753,78355329,312723717,656197893,1089399836,2723474460,4196236289,2416016385,8186515468
%N A298816 a(n) is the binary XOR of all n-bit squares, with a(2)=0 indicating that no 2-bit squares exist.
%C A298816 XOR is the binary exclusive-or operator.
%e A298816 There are two squares whose binary representation is 5 bits long, namely 16 and 25. a(5) = 9 because 25 XOR 16 = 9.
%e A298816 There are four squares whose binary representation is 7 bits long, namely 64, 81, 100 and 121. a(7) = (64 XOR 81 XOR 100 XOR 121) = 12.
%o A298816 (Python)
%o A298816 i = n = x = L = 1
%o A298816 while L < 47:
%o A298816     i+=1
%o A298816     nextn = i*i
%o A298816     if (nextn ^ n) > n:  # if lengths of binary representations are different
%o A298816         print(x, end=', ')
%o A298816         x = 0
%o A298816         prevL = L
%o A298816         L = len(bin(nextn))-2
%o A298816         for j in range(prevL, L-1):  print(0, end=', ')
%o A298816     n = nextn
%o A298816     x ^= n
%Y A298816 Cf. A000290, A007088, A070939.
%K A298816 nonn,base
%O A298816 1,3
%A A298816 _Alex Ratushnyak_, Jan 26 2018