A098195 Starting values x such that the map x -> A098189(x) enters any cycle of length 29.

246, 250, 274, 276, 278, 282, 345, 356, 382, 386, 390, 392, 399, 400, 405, 424, 438, 468, 474, 478, 482, 484, 486, 490, 510, 522, 524, 534, 556, 562, 566, 570, 578, 579, 591, 594, 598, 602, 614, 618, 620, 621, 622, 626, 628, 630, 642, 645, 648, 650, 662

Offset

1,1

Comments

Iterating the map x -> A098189(x) may enter a cycle with 29 members (and there may be distinct cycles each with 29 members). The sequence lists all starting values of x such that (after some transient x) one of these cycles of length 29 is entered.

See other attractors and basins of attracted terms in A098191-A098195.

Corresponding number of transient terms for each term in a(n): {26, 25, 25, 25, 24, 23, 25, 26, 23, 22, 21, 24, 26, 24, 26, 25, 22, 27, 39, 17, 16, 22, 15, 27, 22, 27, 25, 25, 26, 16, 15, 14, 23, 25, 25, 33, 22, 39, 14, 13, 34, 26, 16, 15, 18, 14, 23, 34, 28, 20, 23, ...}. - Michael De Vlieger, Mar 01 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1000

Formula

{x: A098190(x) = 29}.

Example

282 is in the sequence since iterating the map x -> A098189(x) on that number yields 23 transient terms {282, 484, 390, 912, 1072, 628, 478, 482, 486, 570, 1296, 962, 1164, 1576, 998, 1002, 1684, 1270, 1800, 1860, 3360, 5568, 6008} then enters a cycle of 29 terms {3768, 4440, 7056, 6484, 4870, 6840, 9072, 8560, 7624, 4778, 4782, 7984, 4516, 3394, 3398, 3402, 4884, 7680, 10264, 6428, 4828, 4240, 3844, 2950, 3520, 3400, 2932, 2206, 2210}. - Michael De Vlieger, Mar 01 2017

Mathematica

Lookup[#, 29] &@ PositionIndex@ #[[All, -1]] &@ Table[If[n == 1, {0, 1}, Function[s, Function[t, {#, First@ Differences@ Take[Flatten@ t[[# + 1]], 2]} &@ Count[DeleteDuplicates@ t, k_ /; Length@ k == 1]]@ Map[Position[s, #] &, s]]@ NestList[Function[n, DivisorSum[n, # &, CoprimeQ[#, n/#] &] - EulerPhi@ n], n, n + 120]], {n, 800}] (* Michael De Vlieger, Mar 01 2017, Version 10 *)

Crossrefs

Cf. A063919, A098189, A098190, A098191, A098192, A098193, A098194.

Sequence in context: A375324 A259511 A023097 * A214474 A231964 A231965

Adjacent sequences: A098192 A098193 A098194 * A098196 A098197 A098198

Keyword

nonn

Author

Labos Elemer, Sep 03 2004

Extensions

Edited by R. J. Mathar, May 15 2009

Status

approved