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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 (list; graph; refs; listen; history; text; internal format)
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]]

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 A310953

Adjacent sequences:  A180119 A180120 A180121 * A180123 A180124 A180125

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 11 2010

STATUS

approved

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Last modified January 15 10:26 EST 2021. Contains 340187 sequences. (Running on oeis4.)