A180124 Third of three "least, sum, least" self-generating sequences.

3, 5, 8, 11, 14, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 46, 49, 52, 55, 57, 60, 63, 65, 68, 71, 74, 76, 79, 82, 85, 87, 90, 93, 95, 98, 101, 104, 106, 109, 112, 115, 117, 120, 123, 126, 128, 131, 134, 136, 139, 142, 145, 147, 150, 153, 156, 158, 161, 164, 167

Offset

1,1

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

Cf. A180122, A180123.

Sequence in context: A079392 A185723 A022852 * A095375 A345979 A129260

Adjacent sequences: A180121 A180122 A180123 * A180125 A180126 A180127

Keyword

nonn

Author

Clark Kimberling, Aug 11 2010

Status

approved