A182205 Iterate the map in A006368 starting at 40.

40, 60, 90, 135, 101, 76, 114, 171, 128, 192, 288, 432, 648, 972, 1458, 2187, 1640, 2460, 3690, 5535, 4151, 3113, 2335, 1751, 1313, 985, 739, 554, 831, 623, 467, 350, 525, 394, 591, 443, 332, 498, 747, 560, 840, 1260, 1890, 2835, 2126, 3189, 2392, 3588, 5382

Offset: 0

Author

Reinhard Zumkeller, Apr 18 2012

Keywords

• nonn

Comments

Like for iterations with starting points 8 or 14, it is conjectured that also this trajectory never repeats.

References

• D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998; see p. 16.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.

Crossrefs

Cf. A028393, A028395, A180853, A180864, A182205; A028398(6) = 40.

Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.

Programs

Haskell

a182205 n = a182205_list !! n
a182205_list = iterate a006368 40

Mathematica

SubstitutionSystem[{n_ :> If[EvenQ[n], 3 n/2, Round[3 n/4]]}, {40}, 60] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

Formula

a(n+1) = A006368(a(n)), with a(0) = 40.