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.

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

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