A217729 -id:A217729 - cp's OEIS frontend

A223084 Trajectory of 80 under the map n-> A006369(n).

80, 107, 143, 191, 255, 170, 227, 303, 202, 269, 359, 479, 639, 426, 284, 379, 505, 673, 897, 598, 797, 1063, 1417, 1889, 2519, 3359, 4479, 2986, 3981, 2654, 3539, 4719, 3146, 4195, 5593, 7457, 9943, 13257, 8838, 5892, 3928, 5237, 6983, 9311, 12415, 16553, 22071

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:=proc(N) if N mod 3 = 0 then 2*(N/3); elif N mod 3 = 2 then 4*((N+1)/3)-1; else 4*((N+2)/3)-3; fi; end;
t1:=[80];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

t = {80}; While[n = t[[-1]]; s = Switch[Mod[n, 3], 0, 2*n/3, 1, (4*n - 1)/3, 2, (4*n + 1)/3]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* T. D. Noe, Mar 22 2013 *)
SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, , (4n + 1)/3]}, {80}, 60] // Flatten (* _Jean-François Alcover, Mar 01 2019 *)

A223085 Trajectory of 82 under the map n-> A006369(n).

Original entry on oeis.org

82, 109, 145, 193, 257, 343, 457, 609, 406, 541, 721, 961, 1281, 854, 1139, 1519, 2025, 1350, 900, 600, 400, 533, 711, 474, 316, 421, 561, 374, 499, 665, 887, 1183, 1577, 2103, 1402, 1869, 1246, 1661, 2215, 2953, 3937, 5249, 6999, 4666, 6221, 8295, 5530, 7373

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:=proc(N) if N mod 3 = 0 then 2*(N/3); elif N mod 3 = 2 then 4*((N+1)/3)-1; else 4*((N+2)/3)-3; fi; end;
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 = Switch[Mod[n, 3], 0, 2*n/3, 1, (4*n - 1)/3, 2, (4*n + 1)/3]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* T. D. Noe, Mar 22 2013 *)
SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, , (4n + 1)/3]}, {82}, 60] // Flatten (* _Jean-François Alcover, Mar 01 2019 *)
NestList[If[Divisible[#,3],(2#)/3,Floor[(4#)/3+1/2]]&,82,50] (* Harvey P. Dale, Sep 22 2019 *)

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 *)

A223087 Trajectory of 80 under the map n-> A006368(n).

Original entry on oeis.org

80, 120, 180, 270, 405, 304, 456, 684, 1026, 1539, 1154, 1731, 1298, 1947, 1460, 2190, 3285, 2464, 3696, 5544, 8316, 12474, 18711, 14033, 10525, 7894, 11841, 8881, 6661, 4996, 7494, 11241, 8431, 6323, 4742, 7113, 5335, 4001, 3001, 2251, 1688, 2532, 3798, 5697

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:=[80];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

t = {80}; 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]]}, {80}, 100] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

A368227 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006369 map.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 5, 3, 3, 1, 0, 6, 7, 7, 2, 2, 1, 0, 7, 4, 9, 9, 3, 3, 1, 0, 8, 9, 5, 6, 6, 2, 2, 1, 0, 9, 11, 6, 7, 4, 4, 3, 3, 1, 0, 10, 6, 15, 4, 9, 5, 5, 2, 2, 1, 0, 11, 13, 4, 10, 5, 6, 7, 7, 3, 3, 1, 0, 12, 15, 17, 5, 13, 7, 4, 9, 9, 2, 2, 1, 0

Offset: 0

Paolo Xausa, Dec 18 2023

			Array begins:
  [ 0]   0,  0,  0,  0,  0,  0,  0,  0,  0,   0,  0, ... = A000004
  [ 1]   1,  1,  1,  1,  1,  1,  1,  1,  1,   1,  1, ... = A000012
  [ 2]   2,  3,  2,  3,  2,  3,  2,  3,  2,   3,  2, ... = A010693
  [ 3]   3,  2,  3,  2,  3,  2,  3,  2,  3,   2,  3, ... = A176059
  [ 4]   4,  5,  7,  9,  6,  4,  5,  7,  9,   6,  4, ... = A094328
  [ 5]   5,  7,  9,  6,  4,  5,  7,  9,  6,   4,  5, ... = A094328 (shifted)
  [ 6]   6,  4,  5,  7,  9,  6,  4,  5,  7,   9,  6, ... = A094328 (shifted)
  [ 7]   7,  9,  6,  4,  5,  7,  9,  6,  4,   5,  7, ... = A094328 (shifted)
  [ 8]   8, 11, 15, 10, 13, 17, 23, 31, 41,  55, 73, ... = A028394
  [ 9]   9,  6,  4,  5,  7,  9,  6,  4,  5,   7,  9, ... = A094328 (shifted)
  [10]  10, 13, 17, 23, 31, 41, 55, 73, 97, 129, 86, ... = A028394 (shifted)
  ...    |   |   |
      A001477|A168222
          A006369

Paolo Xausa, Table of n, a(n) for n = 0..11324 (antidiagonals 1..150 of the array, flattened).
Index entries for sequences related to 3x+1 (or Collatz) problem

Rows: A000004, A000012, A010693, A028394, A028396, A094328, A094329, A176059, A185589, A185590, A217729, A223083, A223084, A223085.
Columns: A001477, A006369, A168222.
Main diagonal: A368228.
Cf. A368179.

A006369[n_]:=If[Divisible[n,3],2n/3,Round[4n/3]];
A368227list[dmax_]:=With[{a=Reverse[Table[NestList[A006369,n-1,dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];
A368227list[15] (* Generates 15 antidiagonals *)

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A223084 Trajectory of 80 under the map n-> A006369(n).

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A223085 Trajectory of 82 under the map n-> A006369(n).

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

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A223087 Trajectory of 80 under the map n-> A006368(n).

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A368227 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006369 map.

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