A353312 - OEIS

%I #13 Apr 14 2022 08:53:33

%S 1,4,103,4,4,103,103,3,103,4,103,3,4,103,3,103,6,103,103,103,3,3,103,

%T 3,103,3,103,4,3,6,103,103,103,3,103,3,4,3,103,103,3,3,3,3,3,103,3,

%U 103,6,3,6,103,6,103,103,103,6,103,3,103,3,103,3,3,3,103,103,103,6,3,3,3,103,103,3,3,3,103,103,3,103

%N Size of the finite cycle eventually reached by iterating A353313, or -1 if no finite cycle is ever reached.

%H Antti Karttunen, <a href="/A353312/b353312.txt">Table of n, a(n) for n = 0..19683</a>

%F a(n) = A353311(n) - A353310(n).

%e Starting from n=2 and iterating A353313, we obtain the following 104 terms [2, 5, 10, 19, 34, 59, 100, 169, 284, 475, 794, 1325, 2210, 3685, 6144, 2048, 3415, 5694, 1898, 3165, 1055, 1760, 2935, 4894, 8159, 13600, 22669, 37784, 62975, 104960, 174935, 291560, 485935, 809894, 1349825, 2249710, 3749519, 6249200, 10415335, 17358894, 5786298, 1928766, 642922, 1071539, 1785900, 595300, 992169, 330723, 110241, 36747, 12249, 4083, 1361, 2270, 3785, 6310, 10519, 17534, 29225, 48710, 81185, 135310, 225519, 75173, 125290, 208819, 348034, 580059, 193353, 64451, 107420, 179035, 298394, 497325, 165775, 276294, 92098, 153499, 255834, 85278, 28426, 47379, 15793, 26324, 43875, 14625, 4875, 1625, 2710, 4519, 7534, 12559, 20934, 6978, 2326, 3879, 1293, 431, 720, 240, 80, 135, 45, 15] before the iteration returns to 5 again, in other words, forming a finite cycle of length 103, therefore a(2) = 103.

%o (PARI)

%o A353313(n) = { my(r=(n%3)); if(!r,n/3,((5*((n-r)/3)) + r + 3)); };

%o A353312(n) = { my(visited = Map()); for(j=1, oo, if(mapisdefined(visited, n), return(j-mapget(visited, n)), mapput(visited, n, j)); n = A353313(n)); };

%Y Cf. A349877, A353310, A353311, A353313.

%K nonn

%O 0,2

%A _Antti Karttunen_, Apr 13 2022