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

Author

Reinhard Zumkeller, Sep 19 2015

Keywords

• nonn
• base
• look

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

Crossrefs

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

Programs

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..]

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 *)