

A048991


Write down the numbers 1,2,3,... but omit any number (such as 12 or 23 or 31 ...) which appears in the concatenation of all earlier terms.


16



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 49, 50, 54, 55, 57, 58, 59, 60, 65, 66, 68, 69, 70, 76, 77, 79, 80, 87, 88, 90, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112
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OFFSET

1,2


REFERENCES

Invented by 10yearold Hannah Rollman.


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
Nick Hobson, Python program for this sequence


EXAMPLE

12 is omitted since we see "1,2" at the beginning of the sequence; 101 is omitted because we can see "10,1[1]"; etc.


MATHEMATICA

Clear[a]; a[1] = 1; s = "1"; a[n_] := a[n] = Catch[ For[k = a[n1] + 1, True, k++, If[ StringFreeQ[s, t = ToString[k]], s = s <> t; Throw[k] ] ] ]; Table[a[n], {n, 1, 75}] (* JeanFrançois Alcover, Jan 09 2013 *)


PROG

(Python) see Hobson link
(Haskell)
import Data.List (isInfixOf)
a048991 n = a048991_list !! (n1)
a048991_list = f [1..] [] where
f (x:xs) ys  xs' `isInfixOf` ys = f xs ys
 otherwise = x : f xs (xs' ++ ys)
where xs' = reverse $ show x
 Reinhard Zumkeller, Dec 05 2011


CROSSREFS

See A048992 for the omitted numbers.
Cf. A105390.
Sequence in context: A031996 A023753 A035332 * A131881 A053460 A065200
Adjacent sequences: A048988 A048989 A048990 * A048992 A048993 A048994


KEYWORD

nonn,nice,base,easy


AUTHOR

Bernardo Recamán (ignotus(AT)hotmail.com)


EXTENSIONS

Edited by Patrick De Geest, Jun 02 2003


STATUS

approved



