A155890 a(n+1) is the least integer > a(n) containing all digits of a(n); a(1)=2.

2, 12, 21, 102, 120, 201, 210, 1002, 1020, 1200, 2001, 2010, 2100, 10002, 10020, 10200, 12000, 20001, 20010, 20100, 21000, 100002, 100020, 100200, 102000, 120000, 200001, 200010, 200100, 201000, 210000, 1000002, 1000020, 1000200, 1002000

Offset

1,1

Comments

From Farideh Firoozbakht: (Start)

We can easily show that:

(1) All terms have digits less than 3.

(2) For m > 1, an m-digit term of S has m-2 zeros, one 1 and one 2.

(3) For m > 1, the set A(m) of m-digit terms of S has 2m-2 members and A(m) = Join[Table[10^(m-1)+2*10^t,{t,0,m-2}],Table[2*10^(m-1)+10^t,{t,0,m-2}]].

(4) For each m, at index n = m^2 - m + 2, the number of digits of a(n) equals 1 + number of digits of a(n-1).

(End)

Links

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

Maple

2, seq(op([seq(10^n+2*10^j, j=0..n-1), seq(2*10^n+10^j, j=0..n-1)]), n=1..6); # Robert Israel, Nov 10 2024

Mathematica

(* Mmca code for generating all terms less than 10^m, m>1 (the first m^2-m+1 terms) - by Farideh Firoozbakht *) n=m; A[n_]:=Join[Table[10^(n-1)+2*10^t, {t, 0, n-2}], Table[2*10^(n-1)+10^t, {t, 0, n-2}]]; v={2}; Do[v=Join[v, A[k]], {k, 2, n}]; v

Crossrefs

Sequence in context: A058413 A053890 A053896 * A213969 A199986 A336528

Adjacent sequences: A155887 A155888 A155889 * A155891 A155892 A155893

Keyword

base,nonn

Author

Eric Angelini, Farideh Firoozbakht, and M. F. Hasler, Feb 01 2009

Status

approved