cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A375266 Irregular triangle read by rows in which row n lists the iterates of the A375265 map from n to 1.

Original entry on oeis.org

1, 2, 1, 3, 1, 4, 2, 1, 5, 16, 8, 4, 2, 1, 6, 2, 1, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 8, 4, 2, 1, 9, 3, 1, 10, 5, 16, 8, 4, 2, 1, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 12, 4, 2, 1, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Offset: 1

Views

Author

Paolo Xausa, Aug 08 2024

Keywords

Comments

By definition the trajectory ends when 1 is reached, so row 1 does not contain the cycle 1 -> 4 -> 2 -> 1.
See A375265 for links.

Examples

			Triangle begins:
   1;
   2,  1;
   3,  1;
   4,  2,  1;
   5, 16,  8,  4,  2,  1;
   6,  2,  1;
   7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10,  5, 16,  8,  4,  2,  1;
   8,  4,  2,  1;
   9,  3,  1;
  10,  5, 16,  8,  4,  2,  1;
  ...

Links

Crossrefs

Cf. A375265, A375267 (# of iterations), A375268 (row sums), A375280 (row maxs).
Cf. A070165, A070168, A235795, A350279, A350548.

Programs

  • Mathematica
    A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[NestWhileList[A375265, #, # > 1 &] &, 15]

A375267 Number of iterations of the A375265 map to reach 1 starting from n, or -1 if 1 is never reached.

Original entry on oeis.org

0, 1, 1, 2, 5, 2, 16, 3, 2, 6, 14, 3, 9, 17, 6, 4, 12, 3, 20, 7, 17, 15, 15, 4, 23, 10, 3, 18, 18, 7, 106, 5, 15, 13, 13, 4, 21, 21, 10, 8, 109, 18, 29, 16, 7, 16, 104, 5, 24, 24, 13, 11, 11, 4, 112, 19, 21, 19, 32, 8, 19, 107, 18, 6, 27, 16, 27, 14, 16, 14, 102
Offset: 1

Views

Author

Paolo Xausa, Aug 09 2024

Keywords

Examples

			a(10) = 6 because the trajectory 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 consists of 6 steps.

Links

Crossrefs

(Row lengths of A375266) - 1.
Cf. A006577, A006666, A375280.

Programs

  • Mathematica
    A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[Length[NestWhileList[A375265, #, # > 1 &]] - 1 &, 100]

A375911 Largest value in the trajectory of 2*n - 1 in the Farkas map (A349407).

Original entry on oeis.org

1, 3, 5, 17, 9, 17, 17, 15, 17, 29, 21, 53, 25, 27, 29, 161, 33, 53, 37, 39, 41, 65, 45, 161, 49, 51, 53, 125, 57, 89, 161, 63, 65, 101, 69, 161, 73, 75, 77, 269, 81, 125, 85, 87, 89, 137, 161, 485, 97, 99, 101, 233, 105, 161, 125, 111, 113, 173, 117, 269, 161
Offset: 1

Views

Author

Paolo Xausa, Sep 02 2024

Keywords

Examples

			a(10) = 29 because 29 is the largest value in the trajectory 19 -> 29 -> 15 -> 5 -> 3 -> 1.

Links

Crossrefs

Cf. A349407, A350279, A375909.
Cf. A025586, A365478, A375280.

Programs

  • Mathematica
    FarkasStep[x_] := Which[Divisible[x, 3], x/3, Mod[x, 4] == 3, (3*x + 1)/2, True, (x + 1)/2];
Array[Max[FixedPointList[FarkasStep, 2*# - 1]] &, 100]

Formula

a(n) = max{A350279(n,k) for 1 <= k <= A375909(n) + 1}.

A375268 Row sums of A375266.

Original entry on oeis.org

1, 3, 4, 7, 36, 9, 288, 15, 13, 46, 259, 19, 119, 302, 51, 31, 214, 27, 519, 66, 309, 281, 633, 39, 658, 145, 40, 330, 442, 76, 101104, 63, 292, 248, 540, 55, 535, 557, 158, 106, 101331, 344, 1338, 325, 96, 679, 100979, 79, 806, 708, 265, 197, 399, 81, 102316, 386
Offset: 1

Views

Author

Paolo Xausa, Aug 09 2024

Keywords

Links

Crossrefs

Cf. A375265, A375266, A375267, A375280.
Cf. A033493, A285098.

Programs

  • Mathematica
    A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[Total[NestWhileList[A375265, #, # > 1 &]] &, 100]

Formula

a(n) = Sum_{k = 1..A375267(n) + 1} A375266(n,k).
Showing 1-4 of 4 results.

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