cp's OEIS Frontend

A350657 a(n) is the greatest value of the orbit of n under repeated application of A350229 (the sum of a number and its balanced ternary digits).

%I A350657 #7 Jan 24 2022 16:12:09
%S A350657 0,2,2,6,6,6,6,8,8,14,14,14,14,16,14,15,16,17,18,20,20,24,24,24,24,26,
%T A350657 26,32,32,32,32,44,32,44,44,44,44,44,44,44,44,44,44,44,44,45,46,47,48,
%U A350657 50,50,51,52,53,54,56,56,60,60,60,60,62,62,68,68,68,68
%N A350657 a(n) is the greatest value of the orbit of n under repeated application of A350229 (the sum of a number and its balanced ternary digits).
%C A350657 The sequence { a(n) - n, n >= 0 } has no upper limit (this because the sequence A065363 can be positive on arbitrarily large intervals).
%e A350657 For n = 9:
%e A350657 - the orbit of 9 contains the following values:
%e A350657   k  v   bter(v)  ds(v)
%e A350657   -  --  -------  -----
%e A350657   0   9      100      1
%e A350657   1  10      101      2
%e A350657   2  12      110      2
%e A350657   3  14     1TTT     -2
%e A350657   4  12      110      2
%e A350657 - so a(9) = max({ 9, 10, 12, 14 }) = 14.
%t A350657 f[n_] := n + Total[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[n, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, k - 3, z}]]; Array[Max@ NestWhileList[f, #, UnsameQ, All] &, 67, 0] (* _Michael De Vlieger_, Jan 15 2022 *)
%o A350657 (PARI) b(n) = my (v=n, d); while (n, n=(n-d=[0,1,-1][1+n%3])/3; v+=d); v
%o A350657 a(n) = my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=b(n)); s[#s]
%Y A350657 Cf. A350229, A350656.
%K A350657 nonn,base
%O A350657 0,2
%A A350657 _Rémy Sigrist_, Jan 10 2022