A353309 The maximum sum of base-3 digits occurring among all numbers reached after n, when iterating map x -> A353313(x) starting from x=n, or -1 if no finite cycle is ever reached.

0, 2, 18, 2, 2, 18, 18, 6, 18, 2, 18, 5, 2, 18, 6, 18, 6, 18, 18, 18, 5, 6, 18, 5, 18, 6, 18, 2, 5, 6, 18, 18, 18, 5, 18, 5, 2, 6, 18, 18, 5, 13, 6, 13, 6, 18, 8, 18, 6, 5, 6, 18, 6, 18, 18, 18, 8, 18, 5, 18, 5, 18, 5, 6, 6, 18, 18, 18, 8, 5, 13, 5, 18, 18, 13, 6, 13, 18, 18, 8, 18, 2, 18, 18, 5, 6, 13, 6, 13, 6

Offset

0,2

Links

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

Example

When starting iterating A353313 from n=7, we obtain -> 14 -> 25 -> 44 -> 75 -> 25 -> 44 -> 75 -> 25 -> etc, ad infinitum. Applying A053735 to all distinct terms encountered after 7, that is [14, 25, 44, 75] gives us base-3 digit sums [4, 5, 6, 5], therefore a(7) = 6, which is the largest sum.

Prog

(PARI)
A053735(n) = sumdigits(n, 3);
A353313(n) = { my(r=(n%3)); if(!r, n/3, ((5*((n-r)/3)) + r + 3)); };
A353309(n) = { my(visited = Map(), m=0); for(j=1, oo, n = A353313(n); m=max(m, A053735(n)); if(mapisdefined(visited, n), return(m), mapput(visited, n, j))); };

Crossrefs

Cf. A053735, A353313.

Cf. also A352895.

Sequence in context: A279883 A266166 A077452 * A113918 A253603 A094048

Adjacent sequences: A353306 A353307 A353308 * A353310 A353311 A353312

Keyword

nonn,look

Author

Antti Karttunen, Apr 13 2022

Status

approved