A225570 The greedy smallest infinite reverse Collatz (3x+1) sequence.

1, 2, 4, 8, 16, 5, 10, 20, 40, 13, 26, 52, 17, 34, 11, 22, 7, 14, 28, 56, 112, 37, 74, 148, 49, 98, 196, 65, 130, 43, 86, 172, 344, 688, 229, 458, 916, 305, 610, 203, 406, 812, 1624, 541, 1082, 2164, 721, 1442, 2884, 961, 1922, 3844, 7688, 15376, 5125, 10250

Offset: 1

Author

David Spies, Jul 29 2013

Keywords

• nonn

Comments

For each a(n) (where n > 4), a(n) = (a(n-1) - 1)/3 if the result is an odd integer not divisible by 3. Otherwise a(n) = 2 * a(n-1).

Going backwards from any term a(n) to a(1), this is the Collatz sequence for a(n). Furthermore, each term in the sequence is the smallest possible term (ignoring multiples of 3) with this property given the previous term.

Multiples of 3 are ignored because after visiting a multiple of 3, subsequent terms can only double.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A014682, A070165.

Programs

Maple

A225570 := proc(n)
    local a;
    option remember;
    if n <= 4  then
        2^(n-1) ;
    else
        a := (procname(n-1)-1)/3 ;
        if type(a,'integer') and type(a,'odd') and modp(a,3) <> 0 then
            return a;
        else
            return procname(n-1)*2 ;
        end if;
    end if;
end proc: # R. J. Mathar, Aug 03 2013

Mathematica

last = 8; Join[{1, 2, 4, 8}, Table[test = (last - 1)/3; If[OddQ[last] || ! IntegerQ[test] || IntegerQ[test/3], last = 2*last, last = (last - 1)/3]; last, {96}]] (* T. D. Noe, Aug 11 2013 *)