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A233694 Position of n in the sequence (or tree) S generated in order by these rules: 0 is in S; if x is in S then x + 1 is in S; if nonzero x is in S then 1/x is in S; if x is in S, then i*x is in S; where duplicates are deleted as they occur. 5
1, 2, 3, 5, 11, 23, 49, 102, 212, 443, 926, 1939, 4064, 8509, 17816, 37303, 78105, 163544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It can be proved using the division algorithm for Gaussian integers that S is the set of Gaussian rational numbers: (b + c*i)/d, where b,c,d are integers and d is not 0.

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

The first 16 numbers generated are as follows: 0, 1, 2, i, 3, 1/2, 2 i, 1 + i, -i, -1, 4, 1/3, 3 i, 3/2, i/2, 1 + 2 i. The positions of the nonnegative integers are 1, 2, 3, 5, 11.

MATHEMATICA

Off[Power::infy]; x = {0}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 1/x, I*x} /. ComplexInfinity -> 0]]], {18}]; On[Power::infy]; t1 = Flatten[Position[x, _?(IntegerQ[#] && NonNegative[#] &)]]    (* A233694 *)

t2 = Flatten[Position[x, _?(IntegerQ[#] && Negative[#] &)]]  (* A233695 *)

t = Union[t1, t2]  (* A233696 *)

(* Peter J. C. Moses, Dec 21 2013 *)

CROSSREFS

Cf. A233695, A233696, A232559, A226130, A232723, A226080.

Sequence in context: A162278 A173927 A027763 * A261810 A176499 A175234

Adjacent sequences:  A233691 A233692 A233693 * A233695 A233696 A233697

KEYWORD

nonn,more

AUTHOR

Clark Kimberling, Dec 19 2013

STATUS

approved

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Last modified March 25 19:41 EDT 2017. Contains 284082 sequences.