A262356 a(1) = 1; for n > 1, let s denote the digit-string of a(n-1) with the first digit omitted. Then a(n) is the smallest number not yet present which starts with s, omitting leading zeros.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 13, 30, 14, 40, 15, 50, 16, 60, 17, 70, 18, 80, 19, 90, 21, 100, 22, 23, 31, 101, 102, 24, 41, 103, 32, 25, 51, 104, 42, 26, 61, 105, 52, 27, 71, 106, 62, 28, 81, 107, 72, 29, 91, 108, 82, 200, 33, 34, 43, 35, 53

Offset

1,2

Comments

A simplified variation of A262282.

A permutation of the positive integers with inverse A262358;

A262363 and A262371 give the primes and where they occur: A262363(n)=a(A262371(n)).

a(A262393(n)) = A262390(n).

It seems clear that every number will appear, but it would be nice to have a formal proof. - N. J. A. Sloane, Sep 20 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Mathematica

a[1] = 1; a[n_] := a[n] = Module[{s, k}, s = Rest[IntegerDigits[a[n - 1]]] //. {(0).., d__} :> {d}; For[k = 2, True, k++, If[FreeQ[Array[a, n - 1], k], If[s == {0}, Return[k], If[IntegerDigits[k][[1 ;; Length[s]]] == s, Return[k]]]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 12 2019 *)

Prog

(Haskell)
import Data.List (isPrefixOf, delete, genericIndex)
import Data.Set (singleton, notMember, insert)
a262356 n = a262356_list !! (n-1)
a262356_list = 1 : f "" (singleton "1") where
   f xs s = (read ys :: Int) : f (dropWhile (== '0') ys') (insert ys s)
     where ys@(_:ys') = head
             [vs | vs <- zss, isPrefixOf xs vs, notMember vs s]
   zss = map show [2..]

Crossrefs

Cf. A262283, A262282, A262358 (inverse), A262360 (fixed points), A262374 (binary counterpart), A262363 (primes), A262371, A000030, A262390 (starting with 1), A262393.

Sequence in context: A111470 A227508 A246200 * A277861 A173902 A261370

Adjacent sequences: A262353 A262354 A262355 * A262357 A262358 A262359

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Sep 19 2015

Status

approved