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A145829 Square root of squares in A145768 (XOR of squares of the numbers 1..n).

%I A145829 #20 Dec 17 2021 00:54:18
%S A145829 1,4,1,15,0,16,20,31,16,49,65,224,96,96,337,144,720,400,945,625,928,
%T A145829 828,367,928,1889,624,2609,3568,3568,2064,10273,1040,545,12384,12639,
%U A145829 56800,25812,15119,36,864,144383,146463,195440,61391,61072,61072,58128,25872
%N A145829 Square root of squares in A145768 (XOR of squares of the numbers 1..n).
%H A145829 Reinhard Zumkeller, <a href="/A145829/b145829.txt">Table of n, a(n) for n = 1..63</a>
%t A145829 an = 0; Reap[ For[i = 1, i <= 10^6, i++, an = BitXor[an, i^2]; If[IntegerQ[r = Sqrt[an]], Print[r]; Sow[r]]]][[2, 1]] (* _Jean-François Alcover_, Oct 11 2013, translated from Pari *)
%o A145829 (PARI) an=0; for( i=1,10^4, an=bitxor(an,i^2); issquare(an,&an) && print1(an","))
%o A145829 (Haskell)
%o A145829 a145829 n = a145829_list !! (n-1)
%o A145829 a145829_list = map a000196 $ filter ((== 1) . a010052) $ tail a145768_list
%o A145829 -- _Reinhard Zumkeller_, Nov 09 2012
%o A145829 (Python)
%o A145829 from itertools import count, islice
%o A145829 from sympy import integer_nthroot
%o A145829 def A145829gen(): # generator of terms
%o A145829     m = 0
%o A145829     for n in count(1):
%o A145829         m ^= n**2
%o A145829         a, b = integer_nthroot(m,2)
%o A145829         if b: yield a
%o A145829 A145829_list = list(islice(A145829gen(),20)) # _Chai Wah Wu_, Dec 16 2021
%Y A145829 a(n) = A000196( A145828(n)) = A000196( A145768( A145827(n))); A145828 = { a(n)^2 } = A145768 intersect A000290.
%K A145829 easy,nice,nonn
%O A145829 1,2
%A A145829 _M. F. Hasler_, Oct 20 2008