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A180122
First of three "least, sum, least" self-generating sequences.
3
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 11 2010
STATUS
approved