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

1, 4, 104, 4, 4, 103, 105, 5, 104, 4, 103, 4, 5, 106, 4, 103, 6, 105, 106, 103, 3, 6, 108, 3, 105, 3, 104, 5, 3, 6, 104, 108, 110, 5, 103, 3, 6, 14, 116, 107, 3, 54, 5, 57, 3, 103, 7, 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

Offset: 0

Author

Antti Karttunen, Apr 13 2022

Keywords

• nonn
• look

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, therefore a(2) = 104.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683

Crossrefs

Cf. A349877, A353310, A353312, A353313.

Programs

PARI

A353313(n) = { my(r=(n%3)); if(!r,n/3,((5*((n-r)/3)) + r + 3)); };
A353311(n) = { my(visited = Map()); for(j=0, oo, if(mapisdefined(visited, n), return(j), mapput(visited, n, j)); n = A353313(n)); };

Formula

a(n) = A353310(n) + A353312(n).

a(n) > A349877(n) for all n.