A107778 a(1)=7, a(n) = smallest integer not previously used which contains a digit from a(n-1).

7, 17, 1, 10, 0, 20, 2, 12, 11, 13, 3, 23, 21, 14, 4, 24, 22, 25, 5, 15, 16, 6, 26, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70

Offset

1,1

Comments

Cf. A107353 a(1)=0, A107772 a(1)=1, A107773 a(1)=2, A107774 a(1)=3, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107779 a(1)=8, A107780 a(1)=9, A107781 a(1)=10

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

From Robert Israel, Jul 09 2019: (Start)

For n >= 29, it appears that a(n) = n-1 except:

a(i*10^k+j) = i*10^k+j-2 if i=1 and 2<=j<=10, or 2<=i<=8 and 2<=j<=i.

a(i*10^k+1) = i*10^k+i-1 for 2<=i<=8 or i=10.

(End)

Maple

Agenda:= [$0..6, $8..100]: A[1]:= 7: S:= {7}:
for i from 2 do
  found:= false;
  for j from 1 to nops(Agenda) do
    r:= Agenda[j];
    Sr:= convert(convert(r, base, 10), set);
    if Sr intersect S <> {} then
        A[i]:= r;
        Agenda:= subsop(j=NULL, Agenda);
        S:= Sr;
        found:= true;
        break
     fi
   od;
   if not found then break fi;
od:
seq(A[n], n=1..i-1); # Robert Israel, Jul 08 2019

Mathematica

f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ]; Return[Append[l, c]]]; Nest[f, {7}, 70] (* Ray Chandler, Jul 19 2005 *)

Crossrefs

Cf. A107353, A107772, A107773, A107774, A107775, A107776, A107777, A107779, A107780, A107781.

Sequence in context: A375411 A101122 A090535 * A122735 A094464 A224795

Adjacent sequences: A107775 A107776 A107777 * A107779 A107780 A107781

Keyword

base,nonn

Author

Eric Angelini & Zak Seidov, May 24 2005

Status

approved