A133419 Image of n under one application of the "5x+1" map.

6, 1, 1, 2, 26, 3, 36, 4, 3, 5, 56, 6, 66, 7, 5, 8, 86, 9, 96, 10, 7, 11, 116, 12, 126, 13, 9, 14, 146, 15, 156, 16, 11, 17, 176, 18, 186, 19, 13, 20, 206, 21, 216, 22, 15, 23, 236, 24, 246, 25, 17, 26, 266, 27, 276, 28, 19, 29, 296, 30, 306, 31, 21, 32, 326, 33, 336, 34, 23, 35

Offset: 1

Author

N. J. A. Sloane, Nov 27 2007

Keywords

• nonn
• easy

Comments

The 5x+1 map sends x to x/2 if x is even, x/3 if x is odd and divisible by 3, otherwise 5x+1.

Links

• Tomás Oliveira e Silva, The px+1 problem
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A133420.

Programs

Mathematica

Table[If[EvenQ[n], n/2, If[Mod[n, 3] == 0, n/3, 5*n + 1]], {n, 1, 80}] (* Stefan Steinerberger, Feb 16 2008 *)
Table[Which[EvenQ[n],n/2,Divisible[n,3],n/3,True,5n+1],{n,70}] (* Harvey P. Dale, Jul 08 2018 *)

PARI

a(n)=if(n%2,if(n%3,5*n+1,n/3),n/2) \\ Charles R Greathouse IV, Sep 02 2015

Formula

From Chai Wah Wu, Mar 04 2018: (Start)

a(n) = 2*a(n-6) - a(n-12) for n > 12.

G.f.: x*(4*x^10 + x^9 + x^8 + 2*x^7 + 24*x^6 + 3*x^5 + 26*x^4 + 2*x^3 + x^2 + x + 6)/(x^12 - 2*x^6 + 1). (End)

Extensions

More terms from Stefan Steinerberger, Feb 16 2008

Comment clarified by Chai Wah Wu, Mar 04 2018