A097035 Initial values for the iteration of the function f(x) = A063919(x) such that the iteration ends in a 5-cycle, i.e., in A097024.

570, 870, 1230, 1290, 1326, 1482, 1530, 1686, 1698, 1710, 1794, 1866, 1878, 1890, 2058, 2070, 2142, 2154, 2166, 2178, 2238, 2250, 2502, 2802, 2814, 3042, 3222, 3630, 3702, 3714, 3726, 4350, 4494, 4506, 4518, 4914, 5010, 5142, 5154, 5166, 5284, 5418

Offset: 1

Author

Labos Elemer, Aug 30 2004

Keywords

• nonn

Examples

			n = 570: list = {570, 870, 1290, [1878, 1890, 2142, 2178, 1482], 1878}; after 3 transients, a 5-cycle arises.
n = 1230: {1230, 1794, 2238, 2250, 1530, 1710, [1890, 2142, 2178, 1482, 1878]} ; the iteration to the 5-cycle is not necessarily monotone. - _Hartmut F. W. Hoft_, Jan 25 2024
		

Crossrefs

Cf. A002827, A063919, A063991, A097024, A097030-A097037.

Programs

Mathematica

a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *)
a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/;n>1
a097035Q[k_] := Module[{iter=NestWhileList[a063919, k, UnsameQ, All]}, Apply[Subtract, Reverse[Flatten[Position[iter, Last[iter]], 1]]]==5]
a097035[n_] := Select[Range[n], a097035Q]
a097035[5418] (* Hartmut F. W. Hoft, Jan 25 2024 *)