A109718 Periodic sequence with period {0,1,0,3}, or n^3 mod 4.

0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0

Offset: 0

Author

Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005

Keywords

• easy
• nonn

Comments

Since n^(2k+1) mod 4 = n^3 mod 4 for k>1 this sequence also represents n^5 mod 4; and n^7 mod 4; etc.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Crossrefs

n mod 4 = A010873; n^2 mod 4 = A000035.

Cf. A110270; A131743. - Bruno Berselli, Mar 14 2011

Programs

Magma

&cat[[0,1,0,3]: k in [0..26]]; // Bruno Berselli, Mar 14 2011

PARI

a(n)=n^3%4 \\ Charles R Greathouse IV, Apr 06 2016

Sage

[power_mod(n,3,4 )for n in range(0, 105)] # Zerinvary Lajos, Oct 29 2009

Formula

a(n) = n^3 mod 4.

G.f. = (x+3*x^3)/(1-x^4).

a(n) = (n mod 2)*(n mod 4) = (1+(-1)^(n+1))*(2+i^(n+1))/2 with i=sqrt(-1). - Bruno Berselli, Mar 14 2011