login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257980 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 3. 3
3, 1, 2, -1, 4, -2, 5, -4, 6, -3, 9, -10, 8, -5, 11, -9, 13, -12, 14, -13, 15, -11, 19, -21, 17, -14, 20, -19, 21, -18, 24, -25, 23, -17, 29, -33, 25, -23, 27, -22, 32, -31, 33, -35, 31, -27, 35, -34, 36, -29, -6, 37, -30, 44, -49, 39, -37, 41, -26, -7, 49 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Rule 3 follows.  For k >= 1, let  A(k) = {a(1), …, a(k)} and D(k) = {d(1), …, d(k)}.  Begin with k = 1 and nonnegative integers a(1) and d(1).

Step 1:   If there is an integer h such that 1 - a(k) < h < 0 and h is not in D(k) and a(k) + h is not in A(k), let d(k+1) be the least such h, let a(k+1) = a(k) + h, replace k by k + 1, and repeat Step 1; otherwise do Step 2.

Step 2:  Let h be the least positive integer not in D(k) such that a(k) - h is not in A(k).  Let a(k+1) = a(k) + h and d(k+1) = h.  Replace k by k+1 and do Step 1.

See A257905 for a guide to related sequences and conjectures.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 0, d(1) = 3;

a(2) = 1, d(2) = 1;

a(3) = 3, d(3) = 2;

a(4) = 2, d(4) = -1.

MATHEMATICA

{a, f} = {{0}, {3}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];

If[! IntegerQ[tmp[[1]]], tmp = {Last[a] + #, #} &[NestWhile[# + 1 &, 1, ! (! MemberQ[f, #] && ! MemberQ[a, Last[a] - #]) &]]]; AppendTo[a, tmp[[1]]]; AppendTo[f, tmp[[2]]], {120}]; {a, f} (* Peter J. C. Moses, May 14 2015 *)

CROSSREFS

Cf. A257905, A257910.

Sequence in context: A066743 A257915 A257904 * A203531 A324885 A046645

Adjacent sequences:  A257977 A257978 A257979 * A257981 A257982 A257983

KEYWORD

easy,sign

AUTHOR

Clark Kimberling, May 19 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)