OFFSET
1,2
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David Spies, Jul 29 2013
STATUS
approved