A048992 Hannah Rollman's numbers: the numbers excluded from A048991.

12, 23, 31, 34, 41, 42, 45, 51, 52, 53, 56, 61, 62, 63, 64, 67, 71, 72, 73, 74, 75, 78, 81, 82, 83, 84, 85, 86, 89, 91, 92, 93, 94, 95, 96, 97, 98, 101, 111, 113, 121, 122, 123, 131, 141, 151, 161, 171, 181, 191, 192, 201, 202, 210, 211, 212, 213, 214, 215, 216, 217

Offset

1,1

Comments

A105390(n) = number of terms <= n; for n < 740: A105390(n) < n/2. - Reinhard Zumkeller, Apr 04 2005

A116700 is a similar sequence. Note that 21 is missing from the current sequence, because we deleted 12 in computing A048991 and now 21 is no longer "earlier in the sequence". On the other hand 21 is present in A116700. - N. J. A. Sloane, Aug 05 2007

Otherwise said: Numbers which occur in the concatenation of all smaller numbers not listed in this sequence. - M. F. Hasler, Dec 29 2012

Number of terms < 10^n, n = 1, 2, ...: (0, 37, 589, 7046, ...), gives number of n-digit terms as first differences: (37, 552, 6457, ...). - M. F. Hasler, Oct 25 2019

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Nick Hobson, Python program for this sequence

Mathematica

a[0] = 1; s = "1"; a[n_] := a[n] = For[k = a[n-1] + 1, True, k++, If[StringFreeQ[s, t = ToString[k]], s = s <> t, Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 25 2013 *)

Prog

(Python) # see Hobson link
(Haskell)
import Data.List (isInfixOf)
a048992 n = a048992_list !! (n-1)
a048992_list = g [1..] [] where
   g (x:xs) ys | xs' `isInfixOf` ys = x : g xs ys
               | otherwise          = g xs (xs' ++ ys)
               where xs' = reverse $ show x
-- Reinhard Zumkeller, Dec 05 2011
(PARI) D=[]; for(n=1, 999, for(i=0, #D-#d=digits(n), D[i+1..i+#d]!=d || print1(n", ") || next(2)); D=concat(D, d)) \\ M. F. Hasler, Oct 25 2019

Crossrefs

Complement of A048991.

Similar to A116700: "early birds" in the Barbier word A007376 or Champernowne sequence A033307.

Sequence in context: A101104 A330212 A114455 * A088783 A029756 A346508

Adjacent sequences: A048989 A048990 A048991 * A048993 A048994 A048995

Keyword

nonn,nice,base,easy,look

Author

Bernardo Recamán

Extensions

Edited by Patrick De Geest, Jun 02 2003

Status

approved