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 1-3 of 3 results.

A213199 Numbers k whose Collatz (3x+1) trajectory includes at least one term that is greater than k.

Original entry on oeis.org

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83
Offset: 1

Views

Author

Jayanta Basu, Mar 01 2013

Keywords

Examples

			a(1) = 3 because 3 is the first number k whose trajectory goes above k.

Links

Crossrefs

Cf. A033496, A222562, A222597.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100], Max[Collatz[#]] > # &] (* T. D. Noe, Mar 01 2013 *)

A213204 Number of terms of the Collatz (3x+1) trajectory of n that are greater than or equal to n.

Original entry on oeis.org

1, 1, 6, 1, 3, 4, 13, 1, 14, 2, 9, 2, 4, 9, 12, 1, 5, 8, 11, 1, 3, 5, 8, 1, 11, 2, 103, 4, 6, 9, 98, 1, 11, 3, 6, 3, 5, 6, 18, 1, 98, 2, 11, 2, 4, 6, 93, 1, 6, 5, 8, 1, 3, 96, 99, 1, 10, 2, 12, 5, 7, 92, 94, 1, 6, 4, 7, 1, 3, 4, 88, 1, 98, 2, 8, 2, 4, 11, 14
Offset: 1

Views

Author

Jayanta Basu, Mar 01 2013

Keywords

Examples

			For n=3, the Collatz trajectory is 3, 10, 5, 16, 8, 4, 2, 1 and hence a(3)=6.

Links

Crossrefs

Cf. A076228, A222597.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Select[Collatz[n], # >= n &]], {n, 100}]

Formula

a(n) = A222597(n) - 1.

A217731 Numbers n such that in Collatz (3x+1) trajectory of n, the number of terms < n equals number of terms > n.

Original entry on oeis.org

1, 19, 39, 75, 201, 428, 462, 550, 583, 593, 638, 702, 755, 1486, 2395, 3023, 3583, 3867, 5342, 6998, 7419, 8283, 10367, 10447, 10524, 10567, 10879, 11219, 12379, 13647, 13650, 14252, 14561, 14783, 15230, 15871, 16871, 16875, 17121, 17385, 18046, 19279, 19691
Offset: 1

Views

Author

Jayanta Basu, Mar 26 2013

Keywords

Examples

			19 is in the list because Collatz trajectory of 19 is {19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} and number of terms < 19 = 10 = number of terms > 19.

Links

Crossrefs

Cf. A076228, A222597.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; t = {};Do[If[Length[Select[Collatz[n], # < n &]] == Length[Select[Collatz[n], # > n &]], AppendTo[t, n]], {n, 50000}]; t
Showing 1-3 of 3 results.

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

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