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

1, 0, 4, 9, 9, 21, 12, 28, 449, 577, 357, 997, 6085, 14533, 12517, 15077, 121125, 152869, 400028, 1041052, 1290704, 2556368, 4913664, 11950592, 22421376, 63692672, 7674753, 78355329, 312723717, 656197893, 1089399836, 2723474460, 4196236289, 2416016385, 8186515468

Offset: 1

Author

Alex Ratushnyak, Jan 26 2018

Keywords

• nonn
• base

Comments

XOR is the binary exclusive-or operator.

Examples

			There are two squares whose binary representation is 5 bits long, namely 16 and 25. a(5) = 9 because 25 XOR 16 = 9.
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.
		

Crossrefs

Cf. A000290, A007088, A070939.

Programs

Python

i = n = x = L = 1
while L < 47:
    i+=1
    nextn = i*i
    if (nextn ^ n) > n:  # if lengths of binary representations are different
        print(x, end=', ')
        x = 0
        prevL = L
        L = len(bin(nextn))-2
        for j in range(prevL, L-1):  print(0, end=', ')
    n = nextn
    x ^= n