

A262356


a(1) = 1; for n > 1, let s denote the digitstring of a(n1) with the first digit omitted. Then a(n) is the smallest number not yet present which starts with s, omitting leading zeros.


9



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
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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}] (* JeanFrançois Alcover, Mar 12 2019 *)


PROG

(Haskell)
import Data.List (isPrefixOf, delete, genericIndex)
import Data.Set (singleton, notMember, insert)
a262356 n = a262356_list !! (n1)
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



