A082010 a(n) = n/2 if n is even, otherwise floor(8*n/5)+1.

0, 2, 1, 5, 2, 9, 3, 12, 4, 15, 5, 18, 6, 21, 7, 25, 8, 28, 9, 31, 10, 34, 11, 37, 12, 41, 13, 44, 14, 47, 15, 50, 16, 53, 17, 57, 18, 60, 19, 63, 20, 66, 21, 69, 22, 73, 23, 76, 24, 79, 25, 82, 26, 85, 27, 89, 28, 92, 29, 95, 30, 98, 31, 101, 32, 105, 33, 108, 34, 111, 35, 114, 36, 117

Offset: 0

Author

N. J. A. Sloane, Oct 06 2009, suggested by postings to the Sequence Fans Mailing List by Yasutoshi Kohmoto and Franklin T. Adams-Watters, Sep 30 2009

Keywords

• nonn

Comments

See A152199 for the orbit of 7 under this map (which includes the orbit of 3, 5, 6, 7, 9, ... as well). - M. F. Hasler, Jun 12 2012

This is the 8/5 map, a particular case of the m/n sequence mentioned by Yasutoshi Kohmoto on the SeqFan list (cf. link), which also includes the Collatz map A014682 (for m/n = 3/2). - M. F. Hasler, Jun 12 2012

Links

• Yasutoshi Kohmoto, 8/5 Sequence, SeqFan list, Sep 30 2009
• OEIS wiki, m/n sequences, _M. F. Hasler_, Jun 12 2012
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1).

Programs

Mathematica

Table[If[EvenQ[n],n/2,Floor[(8n)/5+1]],{n,0,80}] (* or *) LinearRecurrence[ {0,1,0,0,0,0,0,0,0,1,0,-1},{0,2,1,5,2,9,3,12,4,15,5,18},80] (* Harvey P. Dale, Dec 18 2012 *)

PARI

A082010(x)=if(bittest(x,0),8*x\5+1,x\2) \\ M. F. Hasler, Jun 12 2012

Formula

a(n) = +a(n-2) +a(n-10) -a(n-12). G.f.: x*(1+x+x^2)*(x^8+2*x^6-x^5+2*x^4+2*x^2-x+2) / ( (1+x+x^2+x^3+x^4)*(x^4-x^3+x^2-x+1)*(x-1)^2*(1+x)^2 ). - R. J. Mathar, Feb 20 2011