A323708 a(n) is the smallest positive number not yet in the sequence that contains both the smallest and largest digits from a(n-1); a(1)=1.

1, 10, 100, 101, 102, 20, 120, 200, 201, 202, 203, 30, 103, 130, 230, 300, 301, 302, 303, 304, 40, 104, 140, 204, 240, 340, 400, 401, 402, 403, 404, 405, 50, 105, 150, 205, 250, 305, 350, 450, 500, 501, 502, 503, 504, 505, 506, 60, 106, 160, 206, 260, 306, 360

Offset: 1

Author

Enrique Navarrete, Jan 24 2019

Keywords

• nonn
• base

Comments

All terms starting with a(2)=10 must contain the digit 0.

From a(110)=809 onwards all terms must contain the digits 0 and 9.

Note that A011540 can also be defined as the sequence where a(n) is the smallest number not yet in the sequence that contains the smallest digit from a(n-1). See crossrefs.

Examples

			a(2)=10 since 10 is the smallest positive number not yet in the sequence that contains the smallest and largest digit (i.e., 1) from a(1)=1.
a(6)=20 since 20 is the smallest positive number not yet in the sequence that contains the smallest and largest digits from a(5)=102.
		

Crossrefs

Cf. A107353, A011540 (smallest digit only), A286890 (largest digit only), A303605.

Programs

Maple

N:= 1000: # for terms before the first term > N
A[1]:= 1:
S:= [$2..N]:
dmin:= 1: dmax:= 1:
found:= true:
for n from 2 while found do
    found := false;
    for i from 1 to nops(S) do
      L:= convert(convert(S[i],base,10),set);
      if {dmin,dmax} subset L then
         A[n]:= S[i];
         dmax:= max(L);
         dmin:= min(L);
         found:= true;
         S:= subsop(i=NULL, S);
         break
      fi
    od;
od:
convert(A,list); # Robert Israel, Mar 28 2019

Mathematica

Nest[Append[#, Block[{k = 2, d}, While[Nand[FreeQ[#[[All, 1]], k], SubsetQ[Set[d, IntegerDigits[k]], #[[-1, -1]] ]], k++]; {k, {Min@ d, Max@ d}}]] &, {{1, {1, 1}}}, 53][[All, 1]] (* Michael De Vlieger, Jan 27 2019 *)

PARI

getFirstTerms(n)={my(Z=List(),A=List([1]),dd=[0,1],c,m=1);for(k=2,+oo,forvec(y=vector(k,u,[u==1,9]),listput(Z,y);for(i=1,#Z,if(m==n,return(Vec(A)));c=2;for(q=1,2,for(j=1,#Z[i],if(Z[i][j]==dd[q],c--;break)));if(!c,dd[1]=vecmin(Z[i]);dd[2]=vecmax(Z[i]);listput(A,fromdigits(Z[i]));listpop(Z,i);m++;break)),0))} \\ R. J. Cano, Feb 04 2019

PARI

isok(k, vas, dm, dM) = {if (vecsearch(vas, k), return (0)); my(dk = Set(digits(k))); vecsearch(dk, dm) && vecsearch(dk, dM);}
nexta(va, vas, i) = {my(k=1, d=digits(va[i]), dm = vecmin(d), dM = vecmax(d)); while (!isok(k, vas, dm, dM), k++); k;}
lista(nn) = {my(va = vector(nn)); va[1] = 1; my(vas = vecsort(va,,8)); for (n=2, nn, va[n] = nexta(va, vas, n-1); vas = vecsort(va,,8);); va;} \\ Michel Marcus, Feb 05 2019