

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, 342454, 717076, 1501502, 3144024, 6583334, 13784969
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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.
The differences of this sequence give the number of elements in each level of the tree. This means that d(n) = a(n)  a(n1) is at least 1, and is bounded by 3*d(n1), since there are three times as many elements in each level, before we exclude repetitions.  Jack W Grahl, Aug 10 2018


LINKS

Table of n, a(n) for n=0..23.


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


EXTENSIONS

More terms from Jack W Grahl, Aug 10 2018


STATUS

approved



