A332782 a(n) = (a(n-1) XOR a(n-5)) + 1, a(0) = a(1) = a(2) = a(3) = a(4) = 0.

0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 5, 8, 12, 9, 13, 9, 2, 15, 7, 11, 3, 2, 14, 10, 2, 2, 1, 16, 27, 26, 25, 25, 10, 18, 9, 17, 9, 4, 23, 31, 15, 7, 4, 20, 12, 4, 4, 1, 22, 27, 32, 37, 37, 52, 48, 17, 53, 17, 38, 23, 7, 51, 35, 6, 18, 22, 38, 6, 1, 20, 3, 38, 33, 33, 54, 54, 17, 49

Offset: 0

Author

Rok Cestnik, Feb 23 2020

Keywords

• nonn
• base

Examples

			a(5) = (a(4) XOR a(0)) + 1 = (0 XOR 0) + 1 = 0 + 1 = 1.
a(6) = (a(5) XOR a(1)) + 1 = (1 XOR 0) + 1 = 1 + 1 = 2.
a(10) = (a(9) XOR a(5)) + 1 = (101_2 XOR 001_2) + 1 = 100_2 + 1 = 101_2 = 5_10.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65536.
• G. Marsaglia, Xorshift RNGs, Journal of Statistical Software, Vol. 8, Issue 14, Jul 2003.
• Wikipedia, Bitwise operation (XOR).
• Wikipedia, Linear-feedback shift register.
• Wikipedia, Xorshift.

Crossrefs

Cf. A114375 (shift 1), A332780 (shift 2), A332781 (shift 3).

Programs

Maple

a:= proc(n) option remember; `if`(n<5, 0,
       Bits[Xor](a(n-1), a(n-5))+1)
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Mar 09 2020

Mathematica

Nest[Append[#, 1 + BitXor @@ #[[{-1, -5}]] ] &, ConstantArray[0, 5], 75] (* Michael De Vlieger, Feb 23 2020 *)

Python

feedback_delay = 4
a = [0 for i in range(feedback_delay+1)]
for i in range(feedback_delay,100):
    a.append((a[i]^a[i-feedback_delay])+1)