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A302388 a(n) is the least positive integer not yet in the sequence in which the largest digit of a(n-3) appears among its digits; a(1)=1, a(2)=2, a(3)=3.

%I A302388 #10 Apr 19 2018 17:37:54
%S A302388 1,2,3,10,12,13,11,20,23,14,21,30,4,22,31,24,25,32,34,5,33,40,15,35,
%T A302388 41,45,50,42,51,52,43,53,54,44,55,56,46,57,6,16,7,26,36,17,60,61,27,
%U A302388 62,63,37,64,65,47,66,67,70,68,71,72,8,73,74,18,75,76,28,77,78,38,79,48,58,9,80
%N A302388 a(n) is the least positive integer not yet in the sequence in which the largest digit of a(n-3) appears among its digits; a(1)=1, a(2)=2, a(3)=3.
%C A302388 The only fixed points are 1,2,3,99.
%C A302388 Starting from a(87)=89, every term must contain a 9.
%C A302388 First differences are bounded by -64 and 71.
%e A302388 a(7)=11 since the largest digit of a(4)=10 is 1, and 11 is the least positive integer at n=7 that contains 1.
%t A302388 Nest[Append[#, Block[{k = 4, d}, While[Nand[FreeQ[#[[All, 1]], k], MemberQ[Set[d, IntegerDigits[k]], Max[#[[-3, -1]] ] ] ], k++]; {k, d}]] &, Transpose@ {#, IntegerDigits@ #} &@ Range[3], 71][[All, 1]] (* _Michael De Vlieger_, Apr 12 2018 *)
%o A302388 (PARI) firstTerms(m)={my(Seq:list=List([1,2,3]),z,cp,r,ok);cp=vector(10,u,u-1);for(i=4,m,z=vecmax(digits(Seq[i-3]));for(t=1,oo,forvec(y=vector(t,u,[1,#cp]),ok=0;for(j=1,t,if(cp[y[j]]==z,ok=1;break));if(ok,r=fromdigits(vector(t,u,cp[y[u]]));for(w=1,#Seq,if(r==Seq[w],ok=0;break));if(ok,listput(Seq,r);break(2))))));return(Seq)} \\ _R. J. Cano_, Apr 14 2018
%Y A302388 Cf. A286890, A300907.
%K A302388 nonn,base
%O A302388 1,2
%A A302388 _Enrique Navarrete_, Apr 06 2018