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

0,1

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.

Formula

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

Mathematica

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

Prog

(Haskell)
a182205 n = a182205_list !! n
a182205_list = iterate a006368 40

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.

Sequence in context: A035120 A094619 A052475 * A195571 A060672 A204754

Adjacent sequences: A182202 A182203 A182204 * A182206 A182207 A182208

Keyword

nonn

Author

Reinhard Zumkeller, Apr 18 2012

Status

approved