A081246 Triangle in which (2^n+1)st row gives trajectory of x=2^n+1 under the map x -> x/2 if x is even, x -> x+1 if x is odd, stopping when reaching 1.

3, 4, 2, 1, 5, 6, 3, 4, 2, 1, 9, 10, 5, 6, 3, 4, 2, 1, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 257, 258, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 513, 514, 257, 258, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1

Offset

1,1

Comments

This is the 2^n+1 conjecture and is easily proved to converge to 1. The number of steps required to reach 1 is always 2n+2. Since (2^(n)+1+1)/2 = 2^(n-1)+1 (2^(n-1)+1+1)/2 = 2^(n-2)+1 .... (2^(n-n+1)+1+1)/2 = 2^(n-n)+1 = 2 2/2 = 1 thus 1 is guaranteed.

Links

Table of n, a(n) for n=1..108.

Example

n = 5 -> 33,34,17,18,9,10,5,6,3,4,2,1

Maple

pxpr(n) = { for(x=1, n, x1=2^x+1; print1(x1" "); while(x1>1, if(x1%2==0, x1/=2, x1 = x1+1); print1(x1" "); ) ) }

Mathematica

Table[NestWhileList[If[EvenQ[#], #/2, #+1]&, 2^n+1, #!=1&], {n, 10}]//Flatten (* Harvey P. Dale, Jan 05 2019 *)

Crossrefs

Sequence in context: A239678 A136374 A303869 * A264928 A323874 A326765

Adjacent sequences: A081243 A081244 A081245 * A081247 A081248 A081249

Keyword

easy,nonn,tabf

Author

Cino Hilliard, Apr 19 2003

Extensions

Corrected and extended by Harvey P. Dale, Jan 05 2019

Status

approved