A051065 a(n) = A004128(n) mod 2.

0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1

Offset: 0

Author

N. J. A. Sloane and Gary W. Adamson

Keywords

• nonn
• easy
• changed

References

• Letter from Gary W. Adamson concerning Prouhet-Thue-Morse sequence, Nov. 11, 1999.

Links

• Benoit Cloitre, 3^13 steps of the walk using step: turn +90 degrees if a(n)=0, -90 degrees if a(n)=1.

Crossrefs

Cf. A004128, A051066, A051067, A051069.

Programs

Mathematica

Join[{0}, Mod[Accumulate[Table[IntegerExponent[3*n, 3], {n, 1, 100}]], 2]] (* Amiram Eldar, Jun 02 2025 *)

PARI

a(n)=if(n<1,0,(a(n\3)+n)%2) \\ Benoit Cloitre, Nov 21 2013

Python

TOP = 1000
a = [0]*TOP
for n in range(1, TOP):
    print(a[n-1], end=',')
    a[n] = (n + a[n//3]) % 2
# Alex Ratushnyak, Aug 17 2012

Python

def A051065(n):
    c, m, a = 1, 3*n, 0
    for k in range(1,n+1):
        c *= 3
        if c > m:
            break
        a ^= m//c&1
    return a # Chai Wah Wu, Sep 02 2025

Formula

a(0)=0, a(n) = (n + a(floor(n/3))) mod 2. - Alex Ratushnyak, Aug 17 2012

Extensions

More terms from James Sellers, Dec 11 1999