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

1, 4, 1, 15, 0, 16, 20, 31, 16, 49, 65, 224, 96, 96, 337, 144, 720, 400, 945, 625, 928, 828, 367, 928, 1889, 624, 2609, 3568, 3568, 2064, 10273, 1040, 545, 12384, 12639, 56800, 25812, 15119, 36, 864, 144383, 146463, 195440, 61391, 61072, 61072, 58128, 25872

Offset: 1

Author

M. F. Hasler, Oct 20 2008

Keywords

• easy
• nice
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..63

Crossrefs

a(n) = A000196( A145828(n)) = A000196( A145768( A145827(n))); A145828 = { a(n)^2 } = A145768 intersect A000290.

Programs

Haskell

a145829 n = a145829_list !! (n-1)
a145829_list = map a000196 $ filter ((== 1) . a010052) $ tail a145768_list
-- Reinhard Zumkeller, Nov 09 2012

Mathematica

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 *)

PARI

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

Python

from itertools import count, islice
from sympy import integer_nthroot
def A145829gen(): # generator of terms
    m = 0
    for n in count(1):
        m ^= n**2
        a, b = integer_nthroot(m,2)
        if b: yield a
A145829_list = list(islice(A145829gen(),20)) # Chai Wah Wu, Dec 16 2021