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A332781 a(n) = (a(n-1) XOR a(n-4)) + 1, a(0) = a(1) = a(2) = a(3) = 0. 2
0, 0, 0, 0, 1, 2, 3, 4, 6, 5, 7, 4, 3, 7, 1, 6, 6, 2, 4, 3, 6, 5, 2, 2, 5, 1, 4, 7, 3, 3, 8, 16, 20, 24, 17, 2, 23, 16, 2, 1, 23, 8, 11, 11, 29, 22, 30, 22, 12, 27, 6, 17, 30, 6, 1, 17, 16, 23, 23, 7, 24, 16, 8, 16, 9, 26, 19, 4, 14, 21, 7, 4, 11, 31, 25, 30, 22, 10, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Exclusive or (XOR) is a natural operation for computers. When combined with delayed feedback it can yield very complex behaviour, which can be utilised for pseudorandom number generation [Marsaglia 2003]. Such "linear-feedback shift register" schemes can be implemented with basic computer operations and are hence very fast. Their behaviour is typically periodic with long periods. Analogous procedures are used to generate this sequence, which takes a delayed feedback XOR and adds 1 at each iteration. It appears to be growing, although existence of loops has not been excluded.

LINKS

Table of n, a(n) for n=0..78.

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.

EXAMPLE

a(4) = (a(3) XOR a(0)) + 1 = (0 XOR 0) + 1 = 0 + 1 = 1.

a(5) = (a(4) XOR a(1)) + 1 = (1 XOR 0) + 1 = 1 + 1 = 2.

a(8) = (a(7) XOR a(4)) + 1 = (100_2 XOR 001_2) + 1 = 101_2 + 1 = 110_2 = 6_10.

MATHEMATICA

Nest[Append[#, 1 + BitXor @@ #[[{-1, -4}]] ] &, ConstantArray[0, 4], 75] (* Michael De Vlieger, Feb 23 2020 *)

PROG

(Python)

feedback_delay = 3

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)

CROSSREFS

Cf. A114375 (shift 1), A332780 (shift 2), A332782 (shift 4).

Sequence in context: A328166 A266447 A100700 * A066115 A227788 A222245

Adjacent sequences:  A332778 A332779 A332780 * A332782 A332783 A332784

KEYWORD

nonn,base,look

AUTHOR

Rok Cestnik, Feb 23 2020

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)