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A180123 Second of three "least, sum, least" self-generating sequences. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 01:03 EST 2021. Contains 340443 sequences. (Running on oeis4.)