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

%I #11 Feb 06 2015 12:28:07

%S 1,4,7,9,12,15,18,20,23,26,29,31,34,37,39,42,45,48,50,53,56,59,61,64,

%T 67,70,72,75,78,80,83,86,89,91,94,97,100,102,105,108,111,113,116,119,

%U 121,124,127,130,132,135,138,141,143,146,149,151,154,157,160,162,165,168

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

%H Clark Kimberling, <a href="/A180122/b180122.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 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 11 2010