How to resolve the algorithm Yellowstone sequence step by step in the XPL0 programming language

Published on 12 May 2024 09:40 PM
#Xpl0

How to resolve the algorithm Yellowstone sequence step by step in the XPL0 programming language

Table of Contents

Problem Statement

The Yellowstone sequence, also called the Yellowstone permutation, is defined as: For n <= 3, For n >= 4,

The sequence is a permutation of the natural numbers, and gets its name from what its authors felt was a spiking, geyser like appearance of a plot of the sequence.

a(4) is 4 because 4 is the smallest number following 1, 2, 3 in the sequence that is relatively prime to the entry before it (3), and is not relatively prime to the number two entries before it (2).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Yellowstone sequence step by step in the XPL0 programming language

Source code in the xpl0 programming language

func GCD(N, D);         \Return the greatest common divisor of N and D
int  N, D, R;           \numerator, denominator, remainder
[if D > N then
    [R:=D; D:=N; N:=R]; \swap D and N
while D > 0 do
    [R:= rem(N/D);
    N:= D;
    D:= R;
    ];
return N;
];

int I, A(30+1), N, T;
[for I:= 1 to 3 do A(I):= I;                    \givens
N:= 4;
repeat  T:= 4;
        loop    [if GCD(T, A(N-1)) = 1 and      \relatively prime
                    GCD(T, A(N-2)) # 1 then     \not relatively prime
                        [loop   [for I:= 1 to N-1 do \test if in sequence
                                    if T = A(I) then quit;
                                quit;
                                ];
                        if I = N then           \T is not in sequence so
                            [A(N):= T;          \ add it in
                            N:= N+1;
                            quit;
                            ];
                        ];
                T:= T+1;                        \next trial
                ];
until   N > 30;
for N:= 1 to 30 do
    [IntOut(0, A(N));  ChOut(0, ^ )];
\\for N:= 1 to 100 do Point(N, A(N));           \plot demonstration
]

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