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

Author

Antti Karttunen, Apr 13 2022

Keywords

• nonn
• look

Examples

			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.
		

Links

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

Crossrefs

Cf. A053735, A353313.

Cf. also A352895.

Programs

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))); };