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A233696 Positions of integers 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, 10, 11, 18, 23, 30, 49, 56, 102, 109, 212, 219, 443, 450, 926, 933, 1939, 1946, 4064, 4071, 8509, 8516, 17816, 17823, 37303, 37310, 78105, 78112, 163544, 163551 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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=1..33.

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.  Positions of integers 0, 1, 2, 3, -1, 4,... are 1,2,3,5,10,11,....

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. A233694, A233695, A232559, A226130, A232723, A226080.

Sequence in context: A104427 A259732 A192229 * A002263 A249991 A039022

Adjacent sequences:  A233693 A233694 A233695 * A233697 A233698 A233699

KEYWORD

nonn,more

AUTHOR

Clark Kimberling, Dec 19 2013

EXTENSIONS

Definition and example corrected. - R. J. Mathar, May 06 2017

STATUS

approved

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Last modified April 7 04:08 EDT 2020. Contains 333292 sequences. (Running on oeis4.)