A223088 -id:A223088 - cp's OEIS frontend

A368179 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006368 map.

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 6, 3, 3, 1, 0, 6, 4, 9, 2, 2, 1, 0, 7, 9, 6, 7, 3, 3, 1, 0, 8, 5, 7, 9, 5, 2, 2, 1, 0, 9, 12, 4, 5, 7, 4, 3, 3, 1, 0, 10, 7, 18, 6, 4, 5, 6, 2, 2, 1, 0, 11, 15, 5, 27, 9, 6, 4, 9, 3, 3, 1, 0, 12, 8, 11, 4, 20, 7, 9, 6, 7, 2, 2, 1, 0

Offset: 0

Paolo Xausa, Dec 15 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,  6,  9,  7,  5,  4,  6,  9,  7,  5,  4, ... = A180853
  [ 5]   5,  4,  6,  9,  7,  5,  4,  6,  9,  7,  5, ... = A180853 (shifted)
  [ 6]   6,  9,  7,  5,  4,  6,  9,  7,  5,  4,  6, ... = A180853 (shifted)
  [ 7]   7,  5,  4,  6,  9,  7,  5,  4,  6,  9,  7, ... = A180853 (shifted)
  [ 8]   8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, ... = A028393
  [ 9]   9,  7,  5,  4,  6,  9,  7,  5,  4,  6,  9, ... = A180853 (shifted)
  [10]  10, 15, 11,  8, 12, 18, 27, 20, 30, 45, 34, ... = A180864 (shifted)
  ...    |   |   |
      A001477|A168221
             |
          A006368

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,  A028393, A028395, A094332, A176059, A180853, A180864, A182205, A217218, A223086, A223087, A223088.
Columns: A001477, A006368, A168221.
Main diagonal: A368180.

A006368[n_]:=If[OddQ[n],Floor[(3n+2)/4],3n/2];
A368179list[dmax_]:=With[{a=Reverse[Table[NestList[A006368,n-1,dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];
A368179list[15] (* Generates 15 antidiagonals *)

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

Original entry on oeis.org

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 *)

cp's OEIS Frontend

A368179 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006368 map.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica