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
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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 *)
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