A145828 Squares in A145768 (XOR of squares of the numbers 1...n).

0, 1, 16, 1, 225, 0, 256, 400, 961, 256, 2401, 4225, 50176, 9216, 9216, 113569, 20736, 518400, 160000, 893025, 390625, 861184, 685584, 134689, 861184, 3568321, 389376, 6806881, 12730624, 12730624, 4260096, 105534529

Offset: 1

Author

M. F. Hasler, Oct 20 2008

Keywords

• easy
• nice
• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..97

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

PARI

{a(n) = my(x, m, k); while( mMichael Somos, Aug 05 2014 */

Python

from gmpy2 import is_square
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

Extensions

Edited to start at 0 to match A145768 by Chai Wah Wu, Aug 05 2014