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A353305 The smallest number reached after n when iterating map x -> A353313(x) and starting from x=n, or -1 if no finite cycle is ever reached.

%I A353305 #5 Apr 13 2022 16:50:11
%S A353305 0,1,5,1,1,5,2,14,5,1,5,20,1,5,25,5,16,5,2,5,20,7,5,23,5,25,5,1,28,16,
%T A353305 5,2,5,11,5,20,1,11,5,5,23,20,14,20,25,5,25,5,16,28,16,5,16,5,2,5,16,
%U A353305 5,11,5,20,5,20,7,11,5,5,5,16,23,20,23,5,5,20,25,20,5,5,25,5,1,5,5,28,16,20,16,20,16,5,5
%N A353305 The smallest number reached after n when iterating map x -> A353313(x) and starting from x=n, or -1 if no finite cycle is ever reached.
%e A353305 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, thus after the initial 2, 5 is the smallest number encountered, therefore a(2) = 5.
%o A353305 (PARI)
%o A353305 A353313(n) = { my(r=(n%3)); if(!r,n/3,((5*((n-r)/3)) + r + 3)); };
%o A353305 A353305(n) = { my(visited = Map(), m=0); for(j=1, oo, n = A353313(n); if(!m, m=n, m=min(m,n)); if(mapisdefined(visited, n), return(m), mapput(visited, n, j))); };
%Y A353305 Cf. A353306 (positions of 1's), A353313.
%K A353305 nonn
%O A353305 0,3
%A A353305 _Antti Karttunen_, Apr 13 2022