A006369 -id:A006369 - cp's OEIS frontend

A028393 Iterate the map in A006368 starting at 8.

8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, 43, 32, 48, 72, 108, 162, 243, 182, 273, 205, 154, 231, 173, 130, 195, 146, 219, 164, 246, 369, 277, 208, 312, 468, 702, 1053, 790, 1185, 889, 667, 500, 750, 1125, 844, 1266, 1899, 1424, 2136, 3204, 4806, 7209, 5407

Offset: 0

J. H. Conway

It is conjectured that this trajectory never repeats, but no proof of this has been found. - N. J. A. Sloane, Jul 14 2009

J. H. Conway, Unpredictable iterations, in Proc. Number Theory Conf., Boulder, CO, 1972, pp. 49-52. - N. J. A. Sloane, Oct 04 2012
R. K. Guy, Unsolved Problems in Number Theory, E17. - N. J. A. Sloane, Oct 04 2012
J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 5. [From N. J. A. Sloane, Jan 21 2011]

Markus Sigg, Table of n, a(n) for n = 0..9999 (terms 0..1000 from T. D. Noe)
J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.
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. [From _N. J. A. Sloane_, Jul 14 2009]
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006368, A028394, A180864.
Cf. A028395, A180853, A182205; A028398(4) = 8.
Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.

a028393 n = a028393_list !! n
a028393_list = iterate a006368 8  -- Reinhard Zumkeller, Apr 18 2012

F := proc(n) option remember; if n = 0 then 8 elif 3*F(n-1) mod 2 = 0 then 3*F(n-1)/2 else round(3*F(n-1)/4); fi; end; [ seq(F(i),i=0..80) ];

f[n_?EvenQ] := 3*n/2; f[n_] := Round[3*n/4]; a[0] = 8; a[n_] := a[n] = f[a[n - 1]]; Table[a[n], {n, 0, 52}]  (* Jean-François Alcover, Jun 10 2013 *)

from functools import lru_cache
@lru_cache(maxsize=None)
def F(n):
    if n == 0: return 8
    elif 3*F(n-1)%2 == 0: return 3*F(n-1)//2
    else: return (3*F(n-1)+1)//4
print([F(i) for i in range(81)]) # Michael S. Branicky, Aug 12 2021 after J. H. Conway

a(n+1) = A006368(a(n)).

A180853 Trajectory of 4 under map n->A006368(n).

Original entry on oeis.org

4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5

Offset: 0

N. J. A. Sloane, Jan 22 2011

The trajectory of 8 is a famous unsolved problem - see A028393.

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.

J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1)

Cf. A028397; A028398(3) = 4.

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

a180853 n = a180853_list !! n
a180853_list = iterate a006368 4  -- Reinhard Zumkeller, Apr 18 2012

Table[{4, 6, 9, 7, 5}, {21}] // Flatten   (* Jean-François Alcover, Jun 10 2013 *)
PadRight[{},120,{4,6,9,7,5}] (* Harvey P. Dale, Jul 11 2020 *)

Vec((-4-6*x-9*x^2-7*x^3-5*x^4)/((x-1)*(1+x+x^2+x^3+x^4))+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Periodic with period of length 5.
G.f.: ( -4-6*x-9*x^2-7*x^3-5*x^4 ) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Mar 10 2011
a(n+1) = A006368(a(n)).
a(n) = a(n-5). - Wesley Ivan Hurt, Apr 26 2021

A182205 Iterate the map in A006368 starting at 40.

Original entry on oeis.org

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

Reinhard Zumkeller, Apr 18 2012

nonn

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

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.

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.

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.

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

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

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

A217218 Trajectory of 44 under the map k -> A006368(k).

Original entry on oeis.org

44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59, 44, 66, 99, 74, 111, 83, 62, 93, 70, 105, 79, 59

Offset: 1

N. J. A. Sloane, Oct 04 2012

Periodic with period length 12.

It is believed that this is the longest trajectory that cycles (the others are {1}, {2,3}, {4,6,9,7,5}).

See also references and links in A006368.

Colin Barker, Table of n, a(n) for n = 1..1000
J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.
John L Simons, Cycles and divergent trajectories for a class of permutation sequences, arXiv:2205.10582 [math.NT], 2022.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A006368.

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

a217218 n = a217218_list !! (n-1)
a217218_list = iterate a006368 44  -- Reinhard Zumkeller, Apr 06 2013

&cat[ [44,66,99,74,111,83,62,93,70,105,79,59]: n in [0..9] ]; // Vincenzo Librandi, Jun 28 2015

t={44}; While[n=t[[-1]]; s=If[EvenQ[n], 3*n/2, Round[3*n/4]]; Length[t]<100&&!MemberQ[t, s], AppendTo[t, s]]; t (* Vincenzo Librandi, Jun 28 2015 *)
PadRight[{},120,{44,66,99,74,111,83,62,93,70,105,79,59}] (* Harvey P. Dale, Jul 30 2025 *)

Vec(x*(44 + 66*x + 99*x^2 + 74*x^3 + 111*x^4 + 83*x^5 + 62*x^6 + 93*x^7 + 70*x^8 + 105*x^9 + 79*x^10 + 59*x^11) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^40)) \\ Colin Barker, Aug 16 2019

a(n+1) = A006368(a(n)).
From Colin Barker, Aug 16 2019: (Start)
G.f.: x*(44 + 66*x + 99*x^2 + 74*x^3 + 111*x^4 + 83*x^5 + 62*x^6 + 93*x^7 + 70*x^8 + 105*x^9 + 79*x^10 + 59*x^11) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).
a(n) = a(n-12) for n>12.
(End)

A223088 Trajectory of 82 under the map n-> A006368(n).

Original entry on oeis.org

82, 123, 92, 138, 207, 155, 116, 174, 261, 196, 294, 441, 331, 248, 372, 558, 837, 628, 942, 1413, 1060, 1590, 2385, 1789, 1342, 2013, 1510, 2265, 1699, 1274, 1911, 1433, 1075, 806, 1209, 907, 680, 1020, 1530, 2295, 1721, 1291, 968, 1452, 2178, 3267, 2450, 3675

Offset: 1

N. J. A. Sloane, Mar 22 2013

nonn

It is conjectured that this trajectory does not close on itself.

T. D. Noe, Table of n, a(n) for n = 1..10000
J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.

Cf. A006369, A006368, A182205.

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

f:=n-> if n mod 2 = 0 then 3*n/2 elif n mod 4 = 1 then (3*n+1)/4 else (3*n-1)/4; fi;
t1:=[82];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

t = {82}; While[n = t[[-1]]; s = If[EvenQ[n], 3*n/2, Round[3*n/4]]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* T. D. Noe, Mar 22 2013 *)
SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {82}, 100] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

A265667 Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3).

Original entry on oeis.org

0, 1, 2, 4, 3, 6, 8, 5, 10, 12, 7, 14, 16, 9, 18, 20, 11, 22, 24, 13, 26, 28, 15, 30, 32, 17, 34, 36, 19, 38, 40, 21, 42, 44, 23, 46, 48, 25, 50, 52, 27, 54, 56, 29, 58, 60, 31, 62, 64, 33, 66, 68, 35, 70, 72, 37, 74, 76, 39, 78, 80, 41, 82, 84, 43, 86, 88, 45

Offset: 0

Bruno Berselli, Dec 12 2015 - based on an idea by Paul Curtz

The inverse permutation is given by P(n) = A006368(n-1) + 1, for n >= 1, and P(0) = 0. - Wolfdieter Lang, Sep 21 2021

This permutation is given by A006369(n-1) + 1, with A006369(-1) = -1. Observed by Kevin Ryde. - Wolfdieter Lang, Sep 22 2021

			-------------------------------------------------------------------------
0, 1, 2, 3,  4, 5, 6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ...
+  +  +  +   +  +  +   +   +   +   +   +   +   +   +   +   +   +   +
0, 0, 0, 1, -1, 1, 2, -2,  2,  3, -3,  3,  4, -4,  4,  5, -5,  5,  6, ...
-------------------------------------------------------------------------
0, 1, 2, 4,  3, 6, 8,  5, 10, 12,  7, 14, 16,  9, 18, 20, 11, 22, 24, ...
-------------------------------------------------------------------------

Bruno Berselli, Table of n, a(n) for n = 0..1000
Peter Lynch and Michael Mackey, Parity and Partition of the Rational Numbers, arXiv:2205.00565 [math.NT], 2022. See set F p. 4.
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
Index entries for permutations of the positive (or nonnegative) integers.

Cf. A001477, A006368, A006369, A008738, A032793.
Cf. A064455: n+floor(n/2)*(-1)^(n mod 2).
Cf. A265888: n+floor(n/4)*(-1)^(n mod 4).
Cf. A265734: n+floor(n/5)*(-1)^(n mod 5).

[n+Floor(n/3)*(-1)^(n mod 3): n in [0..70]];

Table[n + Floor[n/3] (-1)^Mod[n, 3], {n, 0, 70}]

[n+floor(n/3)*(-1)^mod(n,3) for n in (0..70)]

G.f.: x*(1 + 2*x + 4*x^2 + x^3 + 2*x^4) / ((1 - x)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-3) - a(n-6).
a(3*k)   = 4*k;
a(3*k+1) = 2*k+1, hence a(3*k+1) = a(3*k)/2 + 1;
a(3*k+2) = 4*k+2, hence a(3*k+2) = 2*a(3*k+1) = a(3*k) + 2.
Sum_{i=0..n} a(i) = A008738(A032793(n+1)).
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + log(2)/4. - Amiram Eldar, Mar 30 2023

A168221 a(n) = A006368(A006368(n)).

Original entry on oeis.org

0, 1, 2, 3, 9, 6, 7, 4, 18, 5, 11, 12, 27, 15, 16, 8, 36, 10, 20, 21, 45, 24, 25, 13, 54, 14, 29, 30, 63, 33, 34, 17, 72, 19, 38, 39, 81, 42, 43, 22, 90, 23, 47, 48, 99, 51, 52, 26, 108, 28, 56, 57, 117, 60, 61, 31, 126, 32, 65, 66, 135, 69, 70, 35, 144, 37, 74, 75, 153, 78, 79, 40

Offset: 0

Reinhard Zumkeller, Nov 20 2009

Inverse integer permutation to A168222;

a(A006369(n)) = A006368(n).

A.H.M. Smeets, Table of n, a(n) for n = 0..20000
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1).

Cf. A006368, A006369, A168222.

Table[Nest[If[OddQ[#],Floor[(3#+2)/4],3#/2]&,n,2],{n,0,100}] (* Paolo Xausa, Dec 15 2023 *)
LinearRecurrence[{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1},{0,1,2,3,9,6,7,4,18,5,11,12,27,15,16,8,36,10,20,21,45,24,25,13},80] (* Harvey P. Dale, Feb 07 2024 *)

def A006368(n):
    if n%2 == 0:
        return 3*(n//2)
    elif n%4 == 1:
        return 3*(n//4)+1
    else:
        return 3*(n+1)//4-1
n = 0
while n < 30:
    print(n,A006368(A006368(n)))
    n = n+1 # A.H.M. Smeets, Aug 14 2019

From Luce ETIENNE, Aug 14 2019: (Start)
a(n) = 2*a(n-16) - a(n-32).
a(n) = (-18*(40*m^7 - 973*m^6 + 9352*m^5 - 45115*m^4 + 114520*m^3 - 145432*m^2 + 75168*m - 10080)*floor(n/8) - m*(332*m^6 - 7973*m^5 + 75236*m^4 - 352835*m^3 + 855008*m^2 - 999992*m + 422664) + m*(4*m^6 - 105*m^5 + 1120*m^4 - 6195*m^3 + 18676*m^2 - 28980*m + 18000)*(-1)^(n/8))/10080 where m = n mod 8.
(End)
From A.H.M. Smeets, Aug 14 2019: (Start)
a(4*n) = 9*n.
a(8*n+1) = a(8*n-1)+1, n > 0.
a(8*n+3) = a(8*n+2)+1.
a(8*n+5) = a(8*n+3)+3 = a(8*n+2)+4.
a(8*n+6) = a(8*n+5)+1 = a(8*n+3)+4 = a(8*n+2)+5.
a(16*n+1) = 9*n+1.
a(16*n+2) = 18*n+2.
a(16*n+3) = a(16*n+2)+1 = 18*n+3.
a(16*n+5) = a(16*n+3)+3 = 18*n+6.
a(16*n+6) = a(16*n+5)+1 = 18*n+7.
a(16*n+7) = (a(16*n+6)+1)/2 = 9*n+4.
a(16*n+9) = 9*n+5.
a(16*n+10) = 2*a(16*n+9)+1 = 18*n+11.
a(16*n+11) = a(16*n+10)+1 = 18*n+12.
a(16*n+13) = a(16*n+11)+3 = 18*n+15.
a(16*n+14) = a(16*n+13) = 18*n+16.
a(16*n+15) = a(16*n+14)/2 = 9*n+8.
From this, (9*n-7)/16 <= a(n) <= 9*n/4.
(End)
From Colin Barker, Aug 23 2019: (Start)
G.f.: x*(1 - x + x^2)*(1 + 3*x + 5*x^2 + 11*x^3 + 12*x^4 + 8*x^5 + 10*x^7 + 14*x^8 + 13*x^9 + 8*x^10 + 13*x^11 + 14*x^12 + 10*x^13 + 8*x^15 + 12*x^16 + 11*x^17 + 5*x^18 + 3*x^19 + x^20) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2*(1 + x^4)^2*(1 + x^8)).
a(n) = a(n-8) + a(n-16) - a(n-24) for n>23.
(End)

A349378 a(n) = A349376(n) + A349377(n).

Original entry on oeis.org

2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 10, 9, 0, 0, -8, 0, -30, 0, -4, 0, 0, 24, 27, 0, 0, 0, 34, 0, -40, 0, -14, -6, 0, 0, -34, 16, -66, 0, -14, 0, 10, 42, 44, 0, 0, 0, 166, 0, 0, -8, 11, 42, -70, 0, -20, 0, -172, 0, -70, 0, 0, -42, -22, 56, -70, 0, -103, 1, 0, 0, 216, 60, 0, 0, 78

Offset: 1

Antti Karttunen, Nov 17 2021

sign

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A006368, A006369, A349376, A349377.

Cf. also A349352, A349369.

A349378(n) = (A349376(n)+A349377(n)); \\ Needs also code from A349376 and A349377.

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A349376(d) * A349377(n/d). [As the sequences are Dirichlet inverses of each other]

A134625 Sum-fill array starting with (1,2,3,4,...).

Original entry on oeis.org

1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 3, 5, 1, 6, 7, 5, 4, 6, 1, 7, 4, 2, 7, 5, 7, 1, 8, 9, 7, 3, 9, 6, 8, 1, 9, 11, 12, 8, 4, 11, 7, 9, 1, 10, 6, 11, 2, 11, 5, 13, 8, 10, 1, 11, 13, 13, 9, 7, 14, 6

Offset: 1

Clark Kimberling, Nov 04 2007

Every row is a permutation of the positive integers. (Row 2) = A006369. The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2. In every row after row n, for each k<=n, k+1 precedes k and all the numbers between k+1 and k exceed k+1.

			Starting with x = row 1, Step 1 gives
y = (1,3,2,5,3,7,4,9,5,11,6,13,...).
Delete the second 3,5,7,... leaving row 2:
(1,3,2,5,7,4,9,11,6,13,...).
Northwest corner:
1 2 3 4 5 6 7 8
1 3 2 5 7 4 9 11
1 4 3 5 2 7 12 11
1 5 4 7 3 8 2 9
1 6 5 9 4 11 7 10.

C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.

Clark Kimberling, Self-Containing Sequences, Selection Functions, and Parasequences, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.

Cf. A134626, A134627, A134628.

Row 1 is the sequence of positive integers. Row n>=2 is produced from row n by the sum-fill operation, defined on an arbitrary infinite or finite sequence x = (x(1), x(2), x(3), ...) by the following two steps: Step 1. Form the sequence x(1), x(1)+x(2), x(2), x(2)+x(3), x(3), x(3)+x(4), ...; i.e., fill the space between x(n) and x(n+1) by their sum. Step 2. Delete duplicates; i.e. letting y be the sequence resulting from Step 1, if y(n+h)=y(n) for some h>=1, then delete y(n+h).

A223086 Trajectory of 64 under the map n-> A006368(n).

Original entry on oeis.org

64, 96, 144, 216, 324, 486, 729, 547, 410, 615, 461, 346, 519, 389, 292, 438, 657, 493, 370, 555, 416, 624, 936, 1404, 2106, 3159, 2369, 1777, 1333, 1000, 1500, 2250, 3375, 2531, 1898, 2847, 2135, 1601, 1201, 901, 676, 1014, 1521, 1141, 856, 1284, 1926, 2889

Offset: 1

N. J. A. Sloane, Mar 22 2013

nonn

It is conjectured that this trajectory does not close on itself.

T. D. Noe, Table of n, a(n) for n = 1..10000
J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.

Cf. A006369, A006368, A182205.

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

f:=n-> if n mod 2 = 0 then 3*n/2 elif n mod 4 = 1 then (3*n+1)/4 else (3*n-1)/4; fi;
t1:=[64];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

t = {64}; While[n = t[[-1]]; s = If[EvenQ[n], 3 n/2, Round[3 n/4]]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* T. D. Noe, Mar 22 2013 *)
SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {64}, 100] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

cp's OEIS Frontend

A028393 Iterate the map in A006368 starting at 8.

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A180853 Trajectory of 4 under map n->A006368(n).

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A182205 Iterate the map in A006368 starting at 40.

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Haskell

Mathematica

Formula

A217218 Trajectory of 44 under the map k -> A006368(k).

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Haskell

Magma

Mathematica

PARI

Formula

A223088 Trajectory of 82 under the map n-> A006368(n).

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Maple

Mathematica

A265667 Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3).

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Magma

Mathematica

Sage

Formula

A168221 a(n) = A006368(A006368(n)).

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