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

0,2

Links

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

Formula

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

Example

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.

Prog

(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)); };

Crossrefs

Cf. A349877, A353310, A353311, A353313.

Sequence in context: A211047 A326087 A091330 * A024056 A353311 A300976

Adjacent sequences: A353309 A353310 A353311 * A353313 A353314 A353315

Keyword

nonn

Author

_Antti Karttunen_, Apr 13 2022

Status

approved