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.

Previous Showing 11-16 of 16 results.

A087261 a(n) = lcm(4n, A025586(4n)), least common multiple of 4n and the largest value in 3x+1 iteration list started at 4n.

Original entry on oeis.org

4, 8, 48, 16, 20, 24, 364, 32, 468, 40, 572, 48, 52, 56, 480, 64, 68, 72, 1672, 80, 84, 88, 3680, 96, 100, 104, 249264, 112, 116, 480, 286192, 128, 132, 136, 1120, 144, 148, 152, 11856, 160, 378512, 168, 8428, 176, 180, 184, 433904, 192, 196, 200, 11832, 208, 212
Offset: 1

Views

Author

Labos Elemer, Sep 09 2003

Keywords

Links

Crossrefs

Cf. A025586, A033496, A087260.

Programs

  • Mathematica
    c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] Table[LCM[4*w, Max[fpl[4*w]]], {w, 1, 256}]

A087258 a(n) = gcd(n, A025586(n)), greatest common divisor of n and largest value in 3x+1 iteration list started at n.

Original entry on oeis.org

1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 5, 16, 1, 2, 1, 20, 1, 2, 1, 24, 1, 2, 1, 4, 1, 10, 1, 32, 1, 2, 5, 4, 1, 2, 1, 40, 1, 2, 1, 4, 1, 2, 1, 48, 1, 2, 1, 52, 1, 2, 1, 56, 1, 2, 1, 20, 1, 2, 1, 64, 1, 2, 1, 68, 1, 10, 1, 72, 1, 2, 5, 4, 1, 2, 1, 80, 1, 2, 1, 84, 1, 2, 1, 88, 1, 2, 1, 4, 1, 2, 1, 96, 1
Offset: 1

Views

Author

Labos Elemer, Sep 09 2003

Keywords

Links

Crossrefs

Cf. A006370, A025586, A033496, A087259, A087260, A087262.

Programs

  • Mathematica
    c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] Table[GCD[w, Max[fpl[w]]], {w, 1, 256}]
  • PARI
    A025586(n) = { my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n), n/=2)); (r); }; \\ From A025586
A087258(n) = gcd(n,A025586(n)); \\ Antti Karttunen, Dec 05 2018

A087259 a(n) = lcm(n, A025586(n)), least common multiple of n and largest value in 3x+1 iteration list started at n.

Original entry on oeis.org

1, 2, 48, 4, 80, 48, 364, 8, 468, 80, 572, 48, 520, 364, 480, 16, 884, 468, 1672, 20, 1344, 572, 3680, 24, 2200, 520, 249264, 364, 2552, 480, 286192, 32, 3300, 884, 1120, 468, 4144, 1672, 11856, 40, 378512, 1344, 8428, 572, 6120, 3680, 433904, 48, 7252, 2200
Offset: 1

Views

Author

Labos Elemer, Sep 09 2003

Keywords

Links

Crossrefs

Cf. A025586, A033496, A087261.

Programs

  • Mathematica
    c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] Table[LCM[w, Max[fpl[w]]], {w, 1, 256}]

A274467 Numbers that are the largest value in the Collatz (3x+1) trajectories of exactly six initial values.

Original entry on oeis.org

16, 232, 340, 448, 1204, 1636, 1960, 2176, 2500, 2608, 3256, 3472, 3688, 3796, 3904, 4336, 4552, 4768, 5092, 5200, 5416, 5632, 5956, 6064, 6496, 6928, 7252, 7360, 7576, 8116, 8548, 8656, 8872, 8980, 9304, 9412, 9520, 9736, 9952, 10168, 10384, 10600, 10708, 10816, 11032, 11464, 11572, 11680
Offset: 1

Views

Author

Hartmut F. W. Hoft, Jun 24 2016

Keywords

Comments

Numbers that appear exactly 6 times in A025586, which gives the largest value in the 3x + 1 trajectory of n. This sequence is a subsequence of A033496 and also of A176869.
There is a single Collatz trajectory containing all initial values to its maximum value n which has the form (8n-20)/9, (4n-10)/9, (2n-5)/9, (2n-2)/3, (n-1)/3, n, where n mod 3 = 1, (2n-2)/3 mod 3 = 1, (4n-10)/9 mod 3 = 0; see also the link in A033496.

Examples

			1636 is in the sequence since it is the largest value in the single trajectory starting with 1452, 726, 363, 1090, 545, 1636, and no other initial values produce a trajectory with maximum 1636.

Links

Crossrefs

Cf. A025586, A033496, A176869, A232870.

Programs

  • Mathematica
    (* function fanSize[] is defined in A105730 *)
a274467[low_, high_] := First[Transpose[Select[Map[{#, fanSize[#]}&, Range[low, high, 4]], Last[#]==6&]]]/; Mod[low, 4]==0
a274467[4,10000] (* Data *)

A275109 Number of times each term of the sequence A025586 (largest value in Collatz trajectory of n) occurs.

Original entry on oeis.org

1, 1, 1, 1, 6, 1, 1, 1, 3, 1, 12, 1, 3, 1, 1, 1, 1, 8, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 13, 1, 1, 1, 3, 1, 8, 1, 3, 1, 1, 1, 6, 1, 3, 3, 1, 1, 1, 1, 3, 1, 1, 14, 1, 1, 1, 1, 1, 6, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 6, 1, 1, 1, 1, 3, 1, 1, 1, 8, 1, 3, 1, 3
Offset: 1

Views

Author

Jaroslav Krizek, Jul 16 2016

Keywords

Comments

The possible values of the sequence A025586 are in A033496. Value A033496(n) occurs exactly a(n) times.

Examples

			a(5) = 6 because there is 6 numbers m such that A025586(m) = A033496(5) = 16: 3, 5, 6, 10, 12 and 16.
See A095387; there is 1579 numbers m such that A025586(m) = 9232 = A033496(940); a(940) = 1579.

Crossrefs

Cf. A025586, A033496.

A375937 Odd numbers which are the largest odd number in their Collatz trajectory.

Original entry on oeis.org

1, 5, 13, 17, 21, 29, 33, 37, 45, 49, 53, 61, 65, 69, 77, 81, 85, 93, 101, 113, 117, 133, 141, 149, 157, 173, 177, 181, 197, 205, 209, 213, 229, 237, 241, 245, 261, 269, 273, 277, 289, 301, 305, 309, 317, 321, 325, 341, 349, 357, 369, 373, 385, 397, 401, 405
Offset: 1

Views

Author

Markus Sigg, Sep 03 2024

Keywords

Comments

a(n) == 1 (mod 4) because the trajectory of 4x+3 is (4x+3, 12x+10, 6x+5, ...) and 6x+5 > 4x+3.

Examples

			The odd elements of the Collatz trajectory (3,10,5,16,8,4,2,1) are {3,5,1} with maximum 5 > 3, so 3 is not a term. The odd elements of the Collatz trajectory (13,40,20,10,5,16,8,4,2,1) are {13,5,1} with maximum 13, so 13 is a term.

Links

Crossrefs

Cf. A033496, A176869.

Programs

  • PARI
    makeEntries(count) = {
    my(L = List(), k = 1);
    while(#L < count,
        my(m = k);
        while(m > 1 && m <= k,
            m = 3*m + 1;
            while(m % 2 == 0, m = m / 2);
        );
        if(m == 1, listput(L, k));
        k += 2
    );
    L
};
print(Vec(makeEntries(56)));

Formula

a(n) = (A176869(n) - 1) / 3 for n > 1.
Previous Showing 11-16 of 16 results.

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