A075487 -id:A075487 - cp's OEIS frontend

A075488 Length of iteration list when Collatz-function is iterated with initial value -1+3^n.

2, 4, 11, 10, 97, 96, 33, 32, 44, 43, 135, 134, 133, 132, 100, 99, 191, 190, 140, 139, 262, 261, 428, 427, 395, 394, 331, 330, 391, 390, 389, 388, 462, 461, 460, 459, 458, 457, 456, 455, 454, 453, 501, 500, 499, 498, 497, 496, 495, 494, 493, 492, 747, 746

Offset: 1

Labos Elemer, Sep 26 2002

nonn

n=3, -1+3^n = 26, list = {26,13,40,20,10,5,16,8,4,2,1}, a(3)=11.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A006370, A008908, A074472, A075484-A075487.

lcoll[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]]; Table[lcoll[3^i - 1], {i, 54}] (* Jayanta Basu, Jun 15 2013 *)

a(n) = A008908(3^n-1).

A075484 Length of iteration-list when Collatz-function(A006370) is iterated with initial value 5^n.

Original entry on oeis.org

1, 6, 24, 109, 26, 124, 147, 139, 100, 92, 115, 337, 135, 277, 181, 261, 240, 219, 286, 322, 451, 337, 303, 432, 243, 540, 408, 444, 304, 464, 438, 554, 484, 582, 517, 677, 462, 617, 1002, 539, 655, 709, 714, 737, 623, 708, 868, 723, 707, 676, 642, 833, 776

Offset: 0

Labos Elemer, Sep 26 2002

nonn

			n=2: 5^n=25, list={25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10.5, 16, 8, 4, 2, 1}, a(2)=24.

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A006370, A008908, A074472, A075485, A075486, A075487, A075488.

Table[Length[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, 5^n, # != 1 &]], {n, 0, 52}] (* Michael De Vlieger, Feb 25 2017 *)

a(n) = A008908(5^n).

A075486 Length of iteration list when Collatz-function is iterated with initial value 2^n + 1.

Original entry on oeis.org

8, 6, 20, 13, 27, 28, 122, 123, 36, 37, 157, 114, 53, 54, 99, 100, 101, 102, 103, 73, 167, 168, 169, 170, 171, 172, 248, 174, 188, 189, 252, 253, 179, 180, 318, 244, 196, 197, 154, 155, 156, 157, 401, 327, 496, 497, 162, 163, 332, 333, 409, 472, 411, 412, 338

Offset: 1

Labos Elemer, Sep 26 2002

nonn

n=4, 1+2^n = 17, list = {17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}, so a(4) = 13.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A006370, A008908, A074472, A075487-A075488.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Collatz[2^n + 1]], {n, 100}] (* T. D. Noe, Jan 17 2013 *)

a(n) = A008908(2^n+1).

A212653 Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n + 1.

Original entry on oeis.org

1, 2, 6, 18, 110, 21, 95, 32, 75, 74, 42, 134, 133, 132, 131, 143, 204, 128, 189, 139, 94, 93, 260, 427, 90, 257, 393, 330, 254, 253, 389, 388, 387, 461, 460, 459, 458, 457, 456, 455, 454, 453, 452, 500, 499, 449, 497, 496, 751, 494, 493, 492, 747, 490, 745

Offset: 0

Michel Lagneau, Feb 14 2013

nonn

It is interesting to note that the quantity 3^k + 1 appears in the formula: A006577(n + 2^A006666(n)) = A006577(n) + A006577(1 + 3^A006667(n)) where A006577 is the n number of halving and tripling steps to reach 1 in '3x+1' problem, A006666 is the number of halving steps to reach 1 and A006667 the number of tripling steps to reach 1.

For example with n = 19, A006577(19 + 2^14) = A006577(19) + A006577(1 + 3^6) => 115 = 20 + 95.

			a(2) = 6 because 3^2 + 1 = 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 with 6 iterations.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Wikipedia, Collatz conjecture

Cf. A006577, A006666, A006667, A034472, A003462, A075487.

f[n_] := Module[{a=3^n+1, k=0}, While[a!=1, k++; If[EvenQ[a], a=a/2, a=a*3+1]]; k]; Table[f[n], {n, 100}]
Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,3^n+1,#!=1&]]-1,{n,0,60}] (* Harvey P. Dale, Sep 26 2015 *)

a(n) = A075487(n) - 1.

A070976 Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with 3^n.

Original entry on oeis.org

0, 7, 19, 111, 22, 96, 33, 76, 75, 43, 135, 134, 133, 132, 144, 205, 129, 190, 140, 95, 94, 261, 428, 91, 258, 394, 331, 255, 254, 390, 389, 388, 462, 461, 460, 459, 458, 457, 456, 455, 454, 453, 501, 500, 450, 498, 497, 752, 495, 494, 493, 748, 491, 746, 489

Offset: 0

Benoit Cloitre, May 17 2002

For all n, it appears that a(n) <= 37n. For n > 22, it appears that a(n) < 16n. - T. D. Noe, Feb 02 2007

This sequence contains some unusually long runs of values that differ by 1. - Dmitry Kamenetsky, Dec 09 2016

			For n=4, 3^4 = 81, and the Collatz sequence (3x + 1 if odd, x/2 if even) goes 81, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1.  This is 22 steps, so a(4) = 22. - _Michael B. Porter_, Dec 15 2016

T. D. Noe, Table of n, a(n) for n = 0..2000

Cf. A279269, A277109. Equals A006577(3^n).

Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,3^n,#>1&]]-1, {n,0,60}] (* Harvey P. Dale, Oct 13 2011 *)

for(n=2,100,s=3^n; t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==1,print1(t,","); ); ))

a(n) = A075487(n+1) = A074472(n) + 1. - T. D. Noe, Feb 02 2007

A075485 Length of iteration list when Collatz-function is iterated with initial value 2^n - 1.

Original entry on oeis.org

1, 8, 17, 18, 107, 108, 47, 48, 62, 63, 157, 158, 159, 160, 130, 131, 225, 226, 178, 179, 304, 305, 474, 475, 445, 446, 385, 386, 449, 450, 451, 452, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 853, 854

Offset: 1

Labos Elemer, Sep 26 2002

nonn

Somewhat surprisingly, these iterations take almost twice as long as the iterations for 2^n + 1. See A075486. - T. D. Noe, Jan 17 2013

			n=4, 2^n - 1 = 15, list = {15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1}, so a(4) = 18.

Cf. A006370, A008908, A074472, A075484, A075486, A075487, A075488.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Collatz[2^n - 1]], {n, 100}] (* T. D. Noe, Jan 17 2013 *)

a(n) = A008908(2^n-1).

A213214 Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n - 1.

Original entry on oeis.org

1, 3, 10, 9, 96, 95, 32, 31, 43, 42, 134, 133, 132, 131, 99, 98, 190, 189, 139, 138, 261, 260, 427, 426, 394, 393, 330, 329, 390, 389, 388, 387, 461, 460, 459, 458, 457, 456, 455, 454, 453, 452, 500, 499, 498, 497, 496, 495, 494, 493, 492, 491, 746, 745, 488

Offset: 1

Michel Lagneau, Mar 02 2013

nonn

It is interesting to note that the quantity 3^n - 1 appears in the Collatz trajectory of 2^n - 1 after n iterations (see the formula).

			a(8) = 31 because A193688(8)=47, and 47 - 2*8 = 31.

Michel Lagneau, Table of n, a(n) for n = 1..1000

Cf. A212653, A075487, A193688.

f[n_]:=Module[{a=3^n-1, k=0}, While[a>1, k++; If[EvenQ[a], a=a/2, a=a*3+1]]; k]; Table[f[n], {n,100}]
Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,3^n-1,#>1&]]-1,{n,100}] (* Harvey P. Dale, Sep 06 2015 *)

a(n) = A193688(n) - 2*n for n > 1.

cp's OEIS Frontend

A075488 Length of iteration list when Collatz-function is iterated with initial value -1+3^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A075484 Length of iteration-list when Collatz-function(A006370) is iterated with initial value 5^n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A075486 Length of iteration list when Collatz-function is iterated with initial value 2^n + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A212653 Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n + 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A070976 Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with 3^n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A075485 Length of iteration list when Collatz-function is iterated with initial value 2^n - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A213214 Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula