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.

A375280 Largest value in the trajectory of n in the A375265 map.

Original entry on oeis.org

1, 2, 3, 4, 16, 6, 52, 8, 9, 16, 52, 12, 40, 52, 16, 16, 52, 18, 88, 20, 52, 52, 160, 24, 88, 40, 27, 52, 88, 30, 9232, 32, 52, 52, 160, 36, 112, 88, 40, 40, 9232, 52, 196, 52, 45, 160, 9232, 48, 148, 88, 52, 52, 160, 54, 9232, 56, 88, 88, 304, 60, 184, 9232, 63
Offset: 1

Views

Author

Paolo Xausa, Aug 09 2024

Keywords

Comments

By definition the trajectory ends when 1 is reached, so a(1) = 1.

Examples

			a(10) = 16 because 16 is the largest value in the trajectory 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.

Links

Crossrefs

Cf. A375265, A375266, A375267.
Cf. A025586, A365478.

Programs

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

Formula

a(n) = max{A375266(n,k) for 1 <= k <= A375267(n) + 1}.

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}.

A365482 In the Collatz (3x+1) problem, values in A006884 for which the maximum excursion ratio (see comments) is greater than 2.

Original entry on oeis.org

27, 319804831, 1410123943, 3716509988199, 9016346070511, 1254251874774375, 10709980568908647, 1980976057694848447
Offset: 1

Views

Author

Paolo Xausa, Sep 05 2023

Keywords

Comments

Kontorovich and Lagarias (2009, 2010) define the maximum excursion ratio as the ratio between the log of the highest point in the trajectory of the T function (started at x) and the log of x, where T(x) is the 3x+1 function = (3x+1)/2 if x is odd, x/2 if x is even (A014682).
They use data from Oliveira e Silva (2010) to compile Table 3 in their paper, but they omit the a(7) = 10709980568908647 value (cf. also Barina and Roosendall links).
Equivalently, values in A006884 for which A365478(A006884(k)) / A006884(k)^2 > 1, for k >= 1.
See A365483 for corresponding maximum excursion values.

Links

Crossrefs

Subsequence of A006884.
Cf. A014682, A365478, A365483.

A365483 In the Collatz (3x+1) problem, maximum excursion values corresponding to the starting points given by A365482.

Original entry on oeis.org

4616, 707118223359971240, 3562942561397226080, 103968231672274974522437732, 126114763591721667597212096, 1823036311464280263720932141024, 175294593968539094415936960141122, 32012333661096566765082938647132369010
Offset: 1

Views

Author

Paolo Xausa, Sep 05 2023

Keywords

Comments

See A365482 for corresponding maximum excursion ratios and additional information.

Links

Crossrefs

Subsequence of A060410.
Cf. A365478, A365482.

Formula

a(n) = A365478(A365482(n)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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