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

1,3

Links

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

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 *)

Prog

(PARI) an=0; for( i=1, 10^4, an=bitxor(an, i^2); issquare(an) && print1(an", "))
(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
(PARI)  {a(n) = my(x, m, k); while( m<n, x = bitxor(x, k++^2); issquare(x) && m++); x}; /* Michael Somos, Aug 05 2014 */

Crossrefs

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

Sequence in context: A099923 A351244 A105671 * A369913 A371081 A223518

Adjacent sequences: A145825 A145826 A145827 * A145829 A145830 A145831

Keyword

easy,nice,nonn

Author

M. F. Hasler, Oct 20 2008

Extensions

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

Status

approved