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

1,2

Links

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

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 *)

Prog

(PARI) an=0; for( i=1, 10^4, an=bitxor(an, i^2); issquare(an, &an) && print1(an", "))
(Haskell)
a145829 n = a145829_list !! (n-1)
a145829_list = map a000196 $ filter ((== 1) . a010052) $ tail a145768_list
-- Reinhard Zumkeller, Nov 09 2012
(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

Crossrefs

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

Sequence in context: A187055 A257501 A096644 * A016115 A164794 A353763

Adjacent sequences: A145826 A145827 A145828 * A145830 A145831 A145832

Keyword

easy,nice,nonn

Author

M. F. Hasler, Oct 20 2008

Status

approved