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A145828 Squares in A145768 (XOR of squares of the numbers 1...n). 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A309132 A099923 A105671 * A223518 A095876 A095851

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

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Last modified January 23 11:42 EST 2022. Contains 350512 sequences. (Running on oeis4.)