A185452 Image of n under the map n -> n/2 if n even, (5*n+1)/2 if n odd.

0, 3, 1, 8, 2, 13, 3, 18, 4, 23, 5, 28, 6, 33, 7, 38, 8, 43, 9, 48, 10, 53, 11, 58, 12, 63, 13, 68, 14, 73, 15, 78, 16, 83, 17, 88, 18, 93, 19, 98, 20, 103, 21, 108, 22, 113, 23, 118, 24, 123, 25, 128, 26, 133, 27, 138, 28, 143, 29, 148, 30, 153, 31, 158, 32, 163, 33, 168, 34, 173, 35, 178, 36, 183, 37, 188, 38, 193, 39, 198

Offset: 0

Author

N. J. A. Sloane, Feb 04 2011

Keywords

• nonn
• easy

References

• J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see pages 11, 88.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A185453, A185454, A185455.

Programs

Magma

[ IsEven(n) select n/2 else (5*n+1)/2: n in [0..79] ]; // Bruno Berselli, Feb 09 2011

Maple

f:=n->if n mod 2 = 0 then n/2 else (5*n+1)/2; fi;

Mathematica

LinearRecurrence[{0,2,0,-1},{0,3,1,8},80] (* Harvey P. Dale, May 16 2014 *)
If[EvenQ[#],#/2,(5#+1)/2]&/@Range[0,80] (* Harvey P. Dale, Jan 02 2015 *)

PARI

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

Formula

a(n) = (6*n+1-(4*n+1)*(-1)^n)/4; g.f.: x*(3+x+2*x^2)/(1-x^2)^2; a(n) = 2*a(n-2)-a(n-4) for n>3. [Bruno Berselli, Feb 09 2011]