A353313 - OEIS

%I #19 Apr 15 2022 10:33:04

%S 0,4,5,1,9,10,2,14,15,3,19,20,4,24,25,5,29,30,6,34,35,7,39,40,8,44,45,

%T 9,49,50,10,54,55,11,59,60,12,64,65,13,69,70,14,74,75,15,79,80,16,84,

%U 85,17,89,90,18,94,95,19,99,100,20,104,105,21,109,110,22,114,115,23,119,120,24,124,125,25,129,130,26

%N If n is of the form 3k, then a(n) = k, and if n is of the form 3k+r, with r = 1 or 2, then a(n) = 5*k + 3 + r.

%C It is conjectured that all iterations of this sequence starting from any n >= 0 will eventually reach a finite cycle, which by necessity then contains at least one multiple of three. See Drozd links and A349876.

%H Antti Karttunen, <a href="/A353313/b353313.txt">Table of n, a(n) for n = 0..19683</a>

%H Nicholas Drozd, <a href="https://nickdrozd.github.io/2021/10/31/busy-beaver-derived.html">A Busy Beaver Champion Derived from Scratch</a>

%H Nicholas Drozd, <a href="https://sites.math.rutgers.edu/~zeilberg/fb155Drozd.txt">Feedback to Doron Zeilberger's opinion #155</a>, Jan. 4, 2022

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

%Y Cf. A349876, A353310, A353311, A353312, A353314 (variant).

%Y Cf. A353305 (the smallest number reached after the starting point n), A353309 (the largest base-3 digit sum reached after the starting point n).

%K nonn

%O 0,2

%A _Antti Karttunen_, Apr 13 2022