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

1,3

Comments

XOR is the binary exclusive-or operator.

Links

Table of n, a(n) for n=1..35.

Example

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.

Prog

(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

Crossrefs

Cf. A000290, A007088, A070939.

Sequence in context: A014719 A139417 A329732 * A095873 A141801 A177083

Adjacent sequences: A298813 A298814 A298815 * A298817 A298818 A298819

Keyword

nonn,base,changed

Author

Alex Ratushnyak, Jan 26 2018

Status

approved