A334042 Write n^2 in binary, interchange 0's and 1's, convert back to decimal.

1, 0, 3, 6, 15, 6, 27, 14, 63, 46, 27, 6, 111, 86, 59, 30, 255, 222, 187, 150, 111, 70, 27, 494, 447, 398, 347, 294, 239, 182, 123, 62, 1023, 958, 891, 822, 751, 678, 603, 526, 447, 366, 283, 198, 111, 22, 1979, 1886, 1791, 1694, 1595, 1494, 1391, 1286, 1179

Offset: 0

Author

Christoph Schreier, Apr 13 2020

Keywords

• nonn
• base
• easy

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A035327.

Programs

Maple

a:= n-> (l-> add((1-l[i])*2^(i-1), i=1..nops(l)))(convert(n, base, 2)):
seq(a(n), n=0..60);  # Alois P. Heinz, Apr 13 2020

Mathematica

a[n_] := FromDigits[1 - IntegerDigits[n^2, 2], 2]; Array[a, 55, 0] (* Amiram Eldar, Apr 13 2020 *)

PARI

a(n)=if(n, my(s=n^2); bitneg(s,exponent(s)+1), 1) \\ Charles R Greathouse IV, Apr 13 2020

Python

def oppsquare(n):
    s = str(bin(n**2))[2:]
    t = ''
    for i in range(len(s)):
        if s[i] == '0':
            t += '1'
        else:
            t += '0'
    return int(t,2)

Python

def A334042(n):
    return 2**(len(bin(n**2))-2)-1-n**2 # Chai Wah Wu, Apr 13 2020

Formula

a(n) = A035327(A000290(n)). - Alois P. Heinz, Apr 13 2020