A318281 - OEIS

%I #11 Oct 22 2018 14:08:17

%S 1,1,1,1,4,1,4,1,4,4,7,1,7,1,7,1,7,4,1,4,1,4,4,7,7,10,1,10,4,7,4,1,4,

%T 4,7,10,10,13,7,1,7,4,13,7,10,7,7,10,13,10,1,10,4,13,7,10,7,10,10,13,

%U 7,13,13,16,10,7,10

%N a(n+1) = a(n-a(n)) if a(n-1) != a(n), otherwise a(n+1) = a(n) + 3; a(1) = a(2) = a(3) = a(4) = 1.

%C Sequences with an analogous condition a(n+1) = a(n) + s for s != 3 tend towards repetitive patterns:

%C   for even values of s this is obvious, e.g.:

%C     s = 2: 1,1,1,3,1,3,1,3,... (1,3 repeats)

%C     s = 4: 1,1,1,1,1,5,1,5,1,5,1,5,... (1,5 repeats)

%C   for odd values of s it has been checked up to s <= 19:

%C     s = 1: 1,1,2,1,2,2,3,1,3,2,1,2,2,3,1,3,... (2,1,2,2,3,1,3 repeats)

%C     s = 5: settles to a repetitive pattern of 192 terms

%C     s = 7: settles to a repetitive pattern of 25 terms

%C     s = 9: settles to a repetitive pattern of 31 terms

%C     s = 11: settles to a repetitive pattern of 37 terms

%C     s = 13: settles to a repetitive pattern of 43 terms

%C     s = 15: settles to a repetitive pattern of 49 terms

%C     s = 17: settles to a repetitive pattern of 55 terms

%C     s = 19: settles to a repetitive pattern of 61 terms

%C   It appears that for further values of s such sequences settle to a repetitive pattern of 4 + 3*s terms.

%H Rok Cestnik, <a href="/A318281/b318281.txt">Table of n, a(n) for n = 1..9999</a>

%e a(5) = a(4) + 3 = 4, because a(3) == a(4).

%e a(6) = a(5-a(5)) = a(1) = 1, because a(4) != a(5).

%o (C)

%o #include<stdio.h>

%o #include<stdlib.h>

%o #include<math.h>

%o int main(void){

%o   int N = 100; //number of terms

%o   int *a = (int*)malloc((N+1)*sizeof(int));

%o   printf("1 1\n2 1\n3 1\n4 1\n");

%o   a[1] = 1;

%o   a[2] = 1;

%o   a[3] = 1;

%o   a[4] = 1;

%o   for(int i = 4; i < N; ++i){

%o     if(a[i-1] != a[i]) a[i+1] = a[i-a[i]];

%o     else a[i+1] = a[i]+3;

%o     printf("%d %d\n", i+1, a[i+1]);

%o   }

%o   free(a);

%o   return 0;

%o }

%Y See A318282 for (a(n)-1)/3.

%Y Cf. A281130, A291598, A004001, A005085, A005229.

%K nonn

%O 1,5

%A _Rok Cestnik_, Aug 23 2018