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A353311 Number of distinct terms encountered when A353313 is iterated, or -1 if the iteration never reaches a finite cycle.

%I A353311 #13 Apr 14 2022 08:53:18
%S A353311 1,4,104,4,4,103,105,5,104,4,103,4,5,106,4,103,6,105,106,103,3,6,108,
%T A353311 3,105,3,104,5,3,6,104,108,110,5,103,3,6,14,116,107,3,54,5,57,3,103,7,
%U A353311 104,6,3,6,106,9,106,107,109,12,104,7,103,3,115,5,7,13,115,109,118,21,3,53,5,106,121,56,3,59,124,105
%N A353311 Number of distinct terms encountered when A353313 is iterated, or -1 if the iteration never reaches a finite cycle.
%H A353311 Antti Karttunen, <a href="/A353311/b353311.txt">Table of n, a(n) for n = 0..19683</a>
%F A353311 a(n) = A353310(n) + A353312(n).
%F A353311 a(n) > A349877(n) for all n.
%e A353311 Starting from n=2 and iterating A353313, we obtain the following 104 terms [2, 5, 10, 19, 34, 59, 100, 169, 284, 475, 794, 1325, 2210, 3685, 6144, 2048, 3415, 5694, 1898, 3165, 1055, 1760, 2935, 4894, 8159, 13600, 22669, 37784, 62975, 104960, 174935, 291560, 485935, 809894, 1349825, 2249710, 3749519, 6249200, 10415335, 17358894, 5786298, 1928766, 642922, 1071539, 1785900, 595300, 992169, 330723, 110241, 36747, 12249, 4083, 1361, 2270, 3785, 6310, 10519, 17534, 29225, 48710, 81185, 135310, 225519, 75173, 125290, 208819, 348034, 580059, 193353, 64451, 107420, 179035, 298394, 497325, 165775, 276294, 92098, 153499, 255834, 85278, 28426, 47379, 15793, 26324, 43875, 14625, 4875, 1625, 2710, 4519, 7534, 12559, 20934, 6978, 2326, 3879, 1293, 431, 720, 240, 80, 135, 45, 15] before the iteration returns to 5 again, therefore a(2) = 104.
%o A353311 (PARI)
%o A353311 A353313(n) = { my(r=(n%3)); if(!r,n/3,((5*((n-r)/3)) + r + 3)); };
%o A353311 A353311(n) = { my(visited = Map()); for(j=0, oo, if(mapisdefined(visited, n), return(j), mapput(visited, n, j)); n = A353313(n)); };
%Y A353311 Cf. A349877, A353310, A353312, A353313.
%K A353311 nonn,look
%O A353311 0,2
%A A353311 _Antti Karttunen_, Apr 13 2022