A368085 -id:A368085 - cp's OEIS frontend

A368159 The n-th term in the trajectory of the n-th prime P under the 'Px+1' map.

2, 10, 13, 5, 336, 111, 19, 215, 1404, 537, 318, 19, 1, 1, 12, 19, 1, 41231, 103, 18, 1, 10, 42, 3120474, 32580, 17, 26, 351348, 260402, 38082, 128, 60457, 138, 140, 547278, 6869, 1, 164, 21, 87, 90, 16245, 12, 194, 33, 90645, 106, 224, 1, 230, 1, 60, 121, 1

Offset: 1

Alois P. Heinz, Dec 13 2023

nonn

See A057684 for definition.

			For n= 4: prime(4)  =  7 ->   50 ->  25 ->   5  = a(4).
For n= 5: prime(5)  = 11 ->  122 ->  61 -> 672 -> 336  = a(5).
For n= 6: prime(6)  = 13 ->  170 ->  85 ->  17 -> 222 -> 111  = a(6).
For n=13: prime(13) = 41 -> 1682 -> 841 ->  29 ->   1 ->  42 ->
                      21 ->    7 ->   1 ->  42 ->  21 ->   7 -> 1 = a(13).

Paolo Xausa, Table of n, a(n) for n = 1..1000

Main diagonal of A368085.

Cf. A000040, A057684, A057689, A057690, A057691.

Px1[p_, n_]:=Catch[For[i=1, iA368159[n_]:=Nest[Px1[Prime[n], #]&, Prime[n],n-1];
Array[A368159,100] (* Paolo Xausa, Dec 14 2023 *)

a(n) = A368085(n,n).

A368113 Trajectory of 7 under the '7x+1' map.

Original entry on oeis.org

7, 50, 25, 5, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1

Offset: 0

Paolo Xausa, Dec 12 2023

See A368085 for definition and cross references.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A368085.

Mathematica
```
PadRight[{7,50,25,5},100,{1,8,4,2}]
```

A368114 Trajectory of 11 under the '11x+1' map.

Original entry on oeis.org

11, 122, 61, 672, 336, 168, 84, 42, 21, 7, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1, 12, 6, 3, 1

Offset: 0

Paolo Xausa, Dec 12 2023

See A368085 for definition and cross references.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A368085.

Mathematica
```
Px1[p_,n_]:=Catch[For[i=1,i
				
```

G.f.: (11 + 122*x + 61*x^2 + 672*x^3 + 325*x^4 + 46*x^5 + 23*x^6 - 630*x^7 - 315*x^8 - 161*x^9 - 83*x^10 - 30*x^11 - 15*x^12 - 4*x^13)/(1 - x^4). - Stefano Spezia, Jun 09 2024

A368115 Trajectory of 17 under the '17x+1' map.

Original entry on oeis.org

17, 290, 145, 29, 494, 247, 19, 324, 162, 81, 27, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1, 18, 9, 3, 1

Offset: 0

Paolo Xausa, Dec 12 2023

See A368085 for definition and cross references.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A368085.

Mathematica
```
Px1[p_,n_]:=Catch[For[i=1,i
				
```

cp's OEIS Frontend

A368159 The n-th term in the trajectory of the n-th prime P under the 'Px+1' map.

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A368113 Trajectory of 7 under the '7x+1' map.

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A368114 Trajectory of 11 under the '11x+1' map.

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A368115 Trajectory of 17 under the '17x+1' map.

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