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A180124 Third of three "least, sum, least" self-generating sequences. 3


%S 3,5,8,11,14,16,19,22,24,27,30,33,35,38,41,44,46,49,52,55,57,60,63,65,

%T 68,71,74,76,79,82,85,87,90,93,95,98,101,104,106,109,112,115,117,120,

%U 123,126,128,131,134,136,139,142,145,147,150,153,156,158,161,164,167

%N Third of three "least, sum, least" self-generating sequences.

%H Clark Kimberling, <a href="/A180124/b180124.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = least positive integer not yet used;

%F b(n) = n + a(n);

%F c(n) = least positive integer not yet used.

%e The three sequences, labeled a,b,c, are

%e a=(1,4,7,9,...), b=(2,6,10,13,...), c=(3,5,8,11...).

%t mex[list_,offset_]:=NestWhile[#+1&,offset,MemberQ[list,#]&];

%t z=100; a[1]=1; b[1]=1+a[1];

%t c[1]=mex[soFar={a[1],b[1]},1];

%t Do[soFar=Join[soFar,{c[n-1]}];

%t a[n]=mex[soFar,c[n-1]];

%t b[n]=n+a[n];soFar=Join[soFar,{a[n],b[n]}];

%t c[n]=mex[soFar,a[n]],{n,2,z}]

%t Map[a,Range[z]](*A180122*)

%t Map[b,Range[z]](*A180123*)

%t Map[c,Range[z]](*A180124*)

%t (* _Peter J. C. Moses_, Aug 22 2014 *)

%t A180122 = Map[Floor[(1 + Sqrt[3]) #] - 1 &, Range[200]]

%t A180123 = A180122 + Range[200]

%t A180124 = Complement[Range[Last[A180122]], Flatten[{A180122, A180123}]]

%t (* _Peter J. C. Moses_, Aug 23 2014 *)

%Y Cf. A180122, A180123.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 11 2010

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Last modified January 18 11:20 EST 2021. Contains 340254 sequences. (Running on oeis4.)