A145828 - OEIS

%I #19 Jul 17 2017 09:37:00

%S 0,1,16,1,225,0,256,400,961,256,2401,4225,50176,9216,9216,113569,

%T 20736,518400,160000,893025,390625,861184,685584,134689,861184,

%U 3568321,389376,6806881,12730624,12730624,4260096,105534529

%N Squares in A145768 (XOR of squares of the numbers 1...n).

%H Chai Wah Wu, <a href="/A145828/b145828.txt">Table of n, a(n) for n = 1..97</a>

%t Reap[For[Sow[x=0]; k=1, k <= 10^4, k++, x = BitXor[x, k^2]; If[IntegerQ[ Sqrt[x]], Sow[x]]]][[2, 1]] (* _Jean-François Alcover_, Nov 25 2015 *)

%o (PARI) an=0; for( i=1,10^4, an=bitxor(an,i^2); issquare(an) && print1(an","))

%o (Python)

%o from gmpy2 import is_square

%o filter(is_square, [reduce(lambda x,y:x^y, [x**2 for x in range(n)]) for n in range(1,10**4)]) # _Chai Wah Wu_, Aug 05 2014

%o (PARI)  {a(n) = my(x, m, k); while( m<n, x = bitxor(x, k++^2); issquare(x) && m++); x}; /* _Michael Somos_, Aug 05 2014 */

%Y Equals A145768 intersect A000290; a(n) = A145768(A145827(n)) = A145829(n)^2.

%K easy,nice,nonn

%O 1,3

%A _M. F. Hasler_, Oct 20 2008

%E Edited to start at 0 to match A145768 by _Chai Wah Wu_, Aug 05 2014