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

Author

Bernardo Recamán

Keywords

• nonn
• nice
• base
• easy
• look

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

Crossrefs

Complement of A048991.

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

Programs

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

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 *)

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

Python

# see Hobson link

Extensions

Edited by Patrick De Geest, Jun 02 2003