

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.


18



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


COMMENTS

Similar to the "punctual birds" A131881, numbers which do not occur earlier than their "natural" position in the string 123...9101112..., but more complex to compute due to the fact that here the omitted numbers must be taken into account. Contains powers of ten A011557 as a subsequence, at indices (1, 10, 63, 402, 2954, ...), giving the number of ndigit terms as (9, 53, 339, 2552, ...).  M. F. Hasler, Oct 25 2019


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.
Since 12 is omitted, 21 does not occur "earlier" and it is in this sequence, but not in A131881, since it occurs earlier in "12,13".  M. F. Hasler, Oct 25 2019


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
(PARI) D=[]; for(n=1, 199, for(i=0, #D#d=digits(n), D[i+1..i+#d]==d && next(2)); print1(n", "); D=concat(D, d)) \\ M. F. Hasler, Oct 25 2019


CROSSREFS

See A048992 for the omitted numbers.
Cf. A105390.
Sequence in context: A023753 A035332 A318536 * A321292 A131881 A053460
Adjacent sequences: A048988 A048989 A048990 * A048992 A048993 A048994


KEYWORD

nonn,nice,base,easy


AUTHOR

Bernardo Recamán


EXTENSIONS

Edited by Patrick De Geest, Jun 02 2003


STATUS

approved



