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]]
(* Peter J. C. Moses, Aug 23 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 11 2010
STATUS
approved