

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
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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



