A180122 First of three "least, sum, least" self-generating sequences.

1, 4, 7, 9, 12, 15, 18, 20, 23, 26, 29, 31, 34, 37, 39, 42, 45, 48, 50, 53, 56, 59, 61, 64, 67, 70, 72, 75, 78, 80, 83, 86, 89, 91, 94, 97, 100, 102, 105, 108, 111, 113, 116, 119, 121, 124, 127, 130, 132, 135, 138, 141, 143, 146, 149, 151, 154, 157, 160, 162, 165, 168

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

a(n) = least positive integer not yet used;

b(n) = n + a(n);

c(n) = least positive integer not yet used.

Example

The three sequences, labeled a,b,c, are
a=(1,4,7,9,...), b=(2,6,10,13,...), c=(3,5,8,11...).

Mathematica

mex[list_, offset_]:=NestWhile[#+1&, offset, MemberQ[list, #]&];
z=100; a[1]=1; b[1]=1+a[1];
c[1]=mex[soFar={a[1], b[1]}, 1];
Do[soFar=Join[soFar, {c[n-1]}];
    a[n]=mex[soFar, c[n-1]];
    b[n]=n+a[n]; soFar=Join[soFar, {a[n], b[n]}];
    c[n]=mex[soFar, a[n]], {n, 2, z}]
Map[a, Range[z]](*A180122*)
Map[b, Range[z]](*A180123*)
Map[c, Range[z]](*A180124*)
(* Peter J. C. Moses, Aug 22 2014 *)
A180122 = Map[Floor[(1 + Sqrt[3]) #] - 1 &, Range[200]]
A180123 = A180122 + Range[200]
A180124 = Complement[Range[Last[A180122]], Flatten[{A180122, A180123}]]
(* Peter J. C. Moses, Aug 23 2014 *)

Crossrefs

Sequence in context: A189526 A184589 A062458 * A080902 A285210 A356056

Adjacent sequences: A180119 A180120 A180121 * A180123 A180124 A180125

Keyword

nonn

Author

Clark Kimberling, Aug 11 2010

Status

approved