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.

A039505 Odd numbers from A039502.

Original entry on oeis.org

17, 21, 23, 25, 31, 33, 37, 41, 45, 49, 55, 61, 67, 73, 83, 91, 99, 109, 111, 117, 123, 131, 147, 153, 163, 165, 175, 179, 185, 195, 197, 209, 213, 219, 221, 225, 229, 233, 239, 243, 247, 257, 261, 263, 267, 277, 279, 291, 293, 295, 305, 311, 313, 319, 321
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Crossrefs

Cf. A037084, A039500-A039504.

Programs

  • Mathematica
    colln[n_]:= NestWhile[If[EvenQ[#], #/2, 3#-1] &, n, FreeQ[{1, 5, 17}, #] &]; Select[Range[1, 321, 2], colln[#] == 17 &] (* Jayanta Basu, Jun 06 2013 *)

A039500 Iterations of "k->k/2 if k is even, k->3k-1 if k is odd" (A001281) starting at these numbers reach 1.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 11, 12, 15, 16, 22, 24, 29, 30, 32, 39, 43, 44, 48, 53, 57, 58, 59, 60, 64, 65, 69, 71, 77, 78, 79, 85, 86, 87, 88, 95, 96, 97, 101, 103, 105, 106, 113, 114, 115, 116, 118, 120, 127, 128, 129, 130, 135, 137, 138, 141, 142, 145, 151, 154, 155, 156
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

It appears that lim_{n->oo} a(n)/n = 5/2. - Benoit Cloitre, Jan 29 2006
Equivalent to the Collatz ('3n+1') problem for negative integers. - Dmitry Kamenetsky, Jan 12 2017
There are 327679 terms in this sequence which are less than 1000000. Based on this, I would suggest that the limit of a(n)/n is more likely to be 3 than 5/2. This is also a natural guess; there are three known periodic orbits for this recurrence. - David Speyer, Mar 25 2022

Links

Crossrefs

Positive integers not in A037084.
Cf. A039501, A039502, A039503, A039504, A039505.

Programs

  • Mathematica
    colln[n_]:= NestWhile[If[EvenQ[#], #/2, 3#-1] &, n, FreeQ[{1, 5, 17}, #] &]; Select[Range[156], colln[#] == 1 &] (* Jayanta Basu, Jun 06 2013 *)

A037084 Positive integers not going to 1 under iterations of the map in A001281: n->3n-1 if n odd, n->n/2 if n even.

Original entry on oeis.org

5, 7, 9, 10, 13, 14, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 61, 62, 63, 66, 67, 68, 70, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 89, 90, 91, 92, 93, 94, 98, 99, 100, 102
Offset: 1

Views

Author

Robert W. Craigen (craigen(AT)fresno.edu)

Keywords

Comments

Up to at least 100000000, every number reaches 1, 5 or 17.
Conjecture : for any x, the iterated process "x ->3x-1" if x is odd or "x ->x/2" if x is even leads to one of the following three cycles: (1, 2), (5, 14, 7, 20, 10), (41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82). - Benoit Cloitre, May 14 2002
Complement (in N*) of A039500 ; union of A039501 and A039502 (conjectured). - M. F. Hasler, Nov 26 2007
Equivalent to the Collatz ('3n+1') problem for negative integers. - Dmitry Kamenetsky, Jan 12 2017

Examples

			Iterations of f starting at 3 are 3,8,4,2,1 - thus 3 is not in the sequence.
Iterations starting at 5 are 5,14,7,20,10,5 -periodic and 1 is not among these values, so 5 is in the sequence.

Links

Crossrefs

Cf. A001281, A039500-A039505.
Cf. A006370, A006577 (Collatz problem: 3n+1).

Programs

  • Mathematica
    colln[n_]:= NestWhile[If[EvenQ[#], #/2, 3#-1] &, n, FreeQ[{1, 5, 17}, #] &]; Select[Range[102], colln[#] != 1 &] (* Jayanta Basu, Jun 06 2013 *)
  • PARI
    A037084( end=999, n=0 /*starting value -1 */)={ for( i=n,end, n=i; while( n > 17 || n > 5 && n < 17, if( n%2, n=3*n-1, n>>=1)); if( n > 4, print1(i", ")))} \\ M. F. Hasler, Nov 26 2007

Extensions

More terms from Christian G. Bower, Feb 15 1999
Edited by M. F. Hasler, Nov 26 2007

A056957 In repeated iterations of function m->m/2 if m even, m->3m-1 if m odd, a(n) is minimum value achieved if starting from n.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 5, 1, 5, 5, 1, 1, 5, 5, 1, 1, 17, 5, 5, 5, 17, 1, 17, 1, 17, 5, 5, 5, 1, 1, 17, 1, 17, 17, 5, 5, 17, 5, 1, 5, 17, 17, 1, 1, 17, 17, 5, 1, 17, 17, 5, 5, 1, 5, 17, 5, 1, 1, 1, 1, 17, 17, 5, 1, 1, 17, 17, 17, 1, 5, 1, 5, 17, 17, 5, 5, 1, 1, 1, 5, 5, 17, 17, 17, 1, 1, 1, 1, 5, 17
Offset: 1

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Comments

At least for n<10000, the only possible cycles reached include 1,2,1,..., 5,14,7,20,10,5,... and 17,50,25,74,37,110,55,164,82,41,122,61,182,91,272,136,68,34,17,... For n<5 only the first occurs, while for n<17 only the first two occur.

Examples

			a(9)=5 since iteration starts: 9, 26, 13, 38, 19, 56, 28, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, ... and 5 is the smallest value

Crossrefs

Cf. A001281. If n is in A039500 then a(n)=1, if n is in A039501 then a(n)=5, if n is in A039502 then a(n)=17. If n is negative then this becomes the 3x+1 problem and the minimum values become those which are most negative (i.e. maximum absolute values) as in A056959.

Formula

a(2n) = a(n)

Extensions

Edited by Bryce Herdt (mathidentity(AT)yahoo.com), Apr 18 2010
Showing 1-4 of 4 results.

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