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