A262360 -id:A262360 - cp's OEIS frontend

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

Reinhard Zumkeller, Sep 19 2015

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

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

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..]

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 *)

A262358 Inverse permutation to A262356.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 13, 28, 30, 31, 35, 39, 43, 47, 51, 55, 15, 32, 38, 60, 61, 63, 65, 67, 69, 71, 17, 36, 42, 62, 77, 78, 80, 82, 84, 86, 19, 40, 46, 64, 79, 89, 90, 92, 94, 96, 21, 44, 50, 66, 81, 91, 99, 100

Offset: 1

Reinhard Zumkeller, Sep 19 2015

A262377 and A262377 give primes and where they occur: A262377(n)=a(A262378(n)).

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (2958 terms from Reinhard Zumkeller)
Index entries for sequences that are permutations of the natural numbers

Cf. A262356, A262360 (fixed points), A262377 (primes), A262378.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a262358 = (+ 1) . fromJust . (`elemIndex` a262356_list)

terms = 100;
(* b = A262356 *) b[1] = 1; b[n_] := b[n] = Module[{s, k}, s = Rest[ IntegerDigits[b[n-1]]] //. {(0).., d__} :> {d}; For[k = 2, True, k++, If[FreeQ[Array[b, n-1], k], If[s == {0}, Return[k], If[IntegerDigits[ k][[1 ;; Length[s]]] == s, Return[k]]]]]];
Sort[Table[{b[n], n}, {n, 1, 2 terms}]][[1 ;; terms, 2]] (* Jean-François Alcover, Mar 12 2019 *)

cp's OEIS Frontend

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.

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