A353312 Size of the finite cycle eventually reached by iterating A353313, or -1 if no finite cycle is ever reached.

1, 4, 103, 4, 4, 103, 103, 3, 103, 4, 103, 3, 4, 103, 3, 103, 6, 103, 103, 103, 3, 3, 103, 3, 103, 3, 103, 4, 3, 6, 103, 103, 103, 3, 103, 3, 4, 3, 103, 103, 3, 3, 3, 3, 3, 103, 3, 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

Offset: 0

Author

Antti Karttunen, Apr 13 2022

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683

Crossrefs

Cf. A349877, A353310, A353311, A353313.

Programs

PARI

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

Formula

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