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.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Apr 13 2022

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A353306 (positions of 1's), A353313.

Programs

PARI

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