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A359218 Let S(n) be the sequence obtained through the mapping of x->A359194(x) starting with n and stopping when 0 is reached, -1 if 0 is never reached. a(n) = m if appears in S(k), k < n, otherwise -1.

%I A359218 #9 Dec 21 2022 22:07:58
%S A359218 0,0,1,0,3,0,6,1,7,4,10,9,10,13,0,15,16,12,18,6,3,21,22,12,24,25,3,27,
%T A359218 21,7,30,31,31,28,34,22,19,37,13,39,40,4,1,43,123,58,46,4,187,49,27,
%U A359218 102,52,96,42,55,87,57,58,21,30,61,48,63,64,60,66,54,51,69
%N A359218 Let S(n) be the sequence obtained through the mapping of x->A359194(x) starting with n and stopping when 0 is reached, -1 if 0 is never reached. a(n) = m if appears in S(k), k < n, otherwise -1.
%C A359218 By convention, a(0) = 0 since n = 0.
%C A359218 Regarding A359215(n), this is the value m that had appeared in S(k), k < n.
%H A359218 Michael De Vlieger, <a href="/A359218/b359218.txt">Table of n, a(n) for n = 0..16384</a>
%H A359218 Michael De Vlieger, <a href="/A359218/a359218.png">Scatterplot of a(n)</a> for n = 0..2^14 and for a(n) <= 2^14, showing a curious pattern that scales with n = 2^k.
%e A359218 a(1) = 0 since S(1) = {1, 0}, but m = 0 appeared in S(0).
%e A359218 a(2) = 1 since S(2) = {2, 1, ...}, but m = 1 appeared in S(1).
%e A359218 a(3) = 0 since S(3) = {3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0}, but m = 0 appeared in S(0).
%e A359218 a(4) = 3 since S(4) = {4, 3, ...} but 3 appears in S(3), etc.
%e A359218 a(5) = 0 since S(5) = {5, 0}, but 0 appears in S(0).
%e A359218 a(6) = 6 since 6 appears in F(3).
%e A359218 a(7) = 1 since S(7) = {7, 10, 1, ...} but 1 appears in S(1).
%e A359218 a(8) = 7 since S(8) = {8, 7, ...} but 7 appears in S(7)
%e A359218 a(9) = 4 since S(9) = {9, 4, ...} but 4 appears in S(4).
%e A359218 a(10) = 10 since 10 appears in S(7).
%e A359218 a(11) = 9 since S(11) = {11, 30, 37, 16, 15, 18, 9, ...} but 9 appears in S(9).
%e A359218 a(12) = 10 since S(12) = {12, 27, ..., 39, 10, ...} but 10 appears in S(7), etc.
%t A359218 c[_] = -1; c[0] = 0; f[n_] := BitXor[3 n, 2^IntegerPart[Log2[3 n] + 1] - 1]; Table[(Map[If[c[#1] == -1, Set[c[#1], #2]] & @@ # &, Partition[#, 2, 1]]; Last@ #) &@ NestWhileList[f, n, c[#] == -1 &], {n, 0, 120}]
%Y A359218 Cf. A359194, A359207, A359215.
%K A359218 base,nonn
%O A359218 0,5
%A A359218 _Michael De Vlieger_, Dec 21 2022