A006884 -id:A006884 - cp's OEIS frontend

A244638 In the '3x+1' problem, primes which as starting values set new records for number of steps to reach 1, where a step means either 'divide by two' or 'triple plus one and then divide by two'.

2, 3, 7, 19, 31, 41, 73, 97, 193, 257, 313, 487, 859, 937, 1249, 2539, 3331, 3947, 5351, 5839, 7963, 9257, 12343, 21943, 31687, 45127, 60169, 78791, 115547, 180463, 213881, 234239, 270271, 376603, 875681, 1023871, 1252663, 1564063, 2585279, 4063723, 5649499, 9973919, 11200681, 39824647, 41464303, 73583071, 95592191, 226588897, 1359533387, 2263333321, 3349304527

Offset: 1

Zak Seidov and Robert G. Wilson v, Jul 03 2014

nonn

Cf. A006877, A006577, A006884.

f[n_] := Length@ NestWhileList[ If[ OddQ@ #, (3 # + 1)/2, #/2] &, n, # > 1 &]  mx = 0; p = 2; lst = {}; While[p < 10^10/2, a = f@ p; If[a > mx, mx = a; Print[{PrimePi@p, p, a - 1}]; AppendTo[ lst, p]]; p = NextPrime@ p]; lst

A224540 Number of numbers k such that all terms of the Collatz (3x+1) iteration of k are <= 3^n.

Original entry on oeis.org

1, 2, 4, 12, 36, 106, 249, 613, 1732, 8028, 23348, 69370, 210807, 634839, 1893582, 5686389, 17031777, 51073675, 153185957, 459516225, 1378707224, 4135278456

Offset: 0

T. D. Noe, Apr 24 2013

			For n = 3, the twelve k are 1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, and 24.

Cf. A006884, A006885, A095384, A224538.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Select[Range[3^n], Max[Collatz[#]] <= 3^n &], {n, 8}]

a(20)-a(21) from Donovan Johnson, Jun 05 2013

A380138 a(n) is the largest value in the '3x+1' trajectory of starting points producing a record number of steps.

Original entry on oeis.org

1, 2, 16, 16, 52, 52, 52, 88, 9232, 9232, 9232, 9232, 9232, 9232, 9232, 9232, 9232, 9232, 250504, 190996, 190996, 250504, 250504, 250504, 481624, 975400, 975400, 497176, 11003416, 11003416, 106358020, 18976192, 41163712, 106358020, 21933016, 104674192, 593279152

Offset: 1

Hugo Pfoertner, Jan 13 2025

nonn

Hugo Pfoertner, Table of n, a(n) for n = 1..148

Cf. A006877, A006878, A006884, A006885, A025586.

s = Map[ToExpression,
  StringSplit[
    Import["https://oeis.org/A006877/b006877.txt", "Data"][[2 ;; -1]]
  ][[All, -1]] ];
Map[Max@ NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, #, # > 1 &] &, s] (* Michael De Vlieger, Jan 13 2025 *)

a(n) = A025586(A006877(n)).

A276665 In the '3x+1' problem, these values for the starting value set new records for both the number of steps and the highest point of trajectory before reaching 1.

Original entry on oeis.org

1, 2, 3, 7, 27, 703, 26623

Offset: 1

José Eduardo Gaboardi de Carvalho, Sep 12 2016

Both the 3x+1 steps and the halving steps are counted.

If it exists, a(7) > 14727207461063895711 (A006877(148)). - Hugo Pfoertner, Jan 12 2025

José Eduardo Gaboardi de Carvalho, Java program

Intersection of A006877 and A006884.

cp's OEIS Frontend

A244638 In the '3x+1' problem, primes which as starting values set new records for number of steps to reach 1, where a step means either 'divide by two' or 'triple plus one and then divide by two'.

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A224540 Number of numbers k such that all terms of the Collatz (3x+1) iteration of k are <= 3^n.

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A380138 a(n) is the largest value in the '3x+1' trajectory of starting points producing a record number of steps.

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Formula

A276665 In the '3x+1' problem, these values for the starting value set new records for both the number of steps and the highest point of trajectory before reaching 1.

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