A180123 Second of three "least, sum, least" self-generating sequences.

2, 6, 10, 13, 17, 21, 25, 28, 32, 36, 40, 43, 47, 51, 54, 58, 62, 66, 69, 73, 77, 81, 84, 88, 92, 96, 99, 103, 107, 110, 114, 118, 122, 125, 129, 133, 137, 140, 144, 148, 152, 155, 159, 163, 166, 170, 174, 178, 181, 185, 189, 193, 196, 200, 204, 207, 211, 215, 219

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 = Flatten[Join[{soFar, c[n - 1]}]];
a[n] = mex[soFar, c[n - 1]]; b[n] = n + a[n];
soFar = Flatten[Join[{soFar, a[n], b[n]}]];
c[n] = mex[soFar, c[n - 1]], {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.

Sequence in context: A144031 A190055 A184929 * A247785 A190701 A184918

Adjacent sequences: A180120 A180121 A180122 * A180124 A180125 A180126

Keyword

nonn

Author

Clark Kimberling, Aug 11 2010

Status

approved