OFFSET
1,2
COMMENTS
The method generalizes: a finite set F={f} of functions f:N->N and finite set G of numbers generate a set S by these rules: (1) every element of G is in S, and (2) if x is in S then f(x) is in S for every f in F. The sequence a results by taking the numbers in S in increasing order.
A191203: 2x, 1+x^2
A191211: 1+2x, 1+x^2
A191281: 2x, x^2-x+1
A191282: 2x, x^2+x+1
A191283: 2x, x(x+1)/2
A191284: floor(3x/2), 2x
A191285: 3x, floor((x^2)/2)
A191286: 3x, 1+x^2
A191287: floor(3x/2), 3x
A191288: 2x, floor((x^2)/3)
A191289: 3x-1, x^2
A191290: 2x+1, x(x+1)/2
For A191203 and other such sequences, the depth g for the NestList in the Mathematica program must be large enough to generate as many terms as required by the user. For example, the rules 2x and 1+x^2, starting with x=1, successively generate set of numbers whose minima are powers of 2: 1->2->4-> ... 2^g -> ....
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
EXAMPLE
1 -> 2 -> 4,5 -> 8,10,17,26 ->
MATHEMATICA
g = 12; Union[Flatten[NestList[{2 #, 1 + #^2} &, 1, g]]]
(* A191203; use g>11 to get all terms up to 4096 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a191203 n = a191203_list !! (n-1)
a191203_list = f $ singleton 1 where
f s = m : f (insert (2 * m) $ insert (m ^ 2 + 1) s')
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 18 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 29 2011
STATUS
approved