A353310 Number of terms encountered when iterating A353313, before reaching the first term that is a part of a finite cycle, or -1 if no finite cycle is ever reached.

0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 1, 1, 3, 1, 0, 0, 2, 3, 0, 0, 3, 5, 0, 2, 0, 1, 1, 0, 0, 1, 5, 7, 2, 0, 0, 2, 11, 13, 4, 0, 51, 2, 54, 0, 0, 4, 1, 0, 0, 0, 3, 3, 3, 4, 6, 6, 1, 4, 0, 0, 12, 2, 4, 10, 12, 6, 15, 15, 0, 50, 2, 3, 18, 53, 0, 56, 21, 2, 3, 0, 2, 5, 19, 0, 0, 62, 1, 59, 2, 2, 27, 65, 6, 5, 5, 8, 90, 8

Offset

0,7

Links

Table of n, a(n) for n=0..98.

Formula

a(n) = A353311(n) - A353312(n).

Example

For n = 1, when iterating with A353313, we obtain 1 -> 4 -> 9 -> 3 -> 1 -> etc, thus 1 itself is included in the closed cycle, and therefore a(1) = 0.
For n = 6, when iterating with A353313, we obtain 6 -> 2 -> 5 -> ..., and after 103 more iterations we obtain 5 again (see examples in A353311 and A353312), thus only the two initial numbers, 6 and 2 are outside of the final closed cycle, therefore a(6) = 2.

Prog

(PARI)
A353313(n) = { my(r=(n%3)); if(!r, n/3, ((5*((n-r)/3)) + r + 3)); };
A353310(n) = { my(visited = Map(), p); for(j=0, oo, if(mapisdefined(visited, n, &p), return(p), mapput(visited, n, j)); n = A353313(n)); };

Crossrefs

Cf. A353311, A353312, A353313.

Sequence in context: A365573 A370278 A369245 * A347883 A024712 A281497

Adjacent sequences: A353307 A353308 A353309 * A353311 A353312 A353313

Keyword

nonn

Author

Antti Karttunen, Apr 14 2022

Status

approved