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%I #46 Jul 01 2021 07:11:08
%S 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,
%T 29,30,32,33,35,36,37,38,39,40,43,44,46,47,48,49,50,54,55,57,58,59,60,
%U 65,66,68,69,70,76,77,79,80,87,88,90,99,100,102,103,104,105,106,107,108,109,110,112
%N 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.
%C 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 n-digit terms as (9, 53, 339, 2552, ...). - _M. F. Hasler_, Oct 25 2019
%D Invented by 10-year-old Hannah Rollman.
%H T. D. Noe, <a href="/A048991/b048991.txt">Table of n, a(n) for n = 1..10000</a>
%H Nick Hobson, <a href="/A048991/a048991.py.txt">Python program for this sequence</a>
%e 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.
%e 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
%t Clear[a]; a[1] = 1; s = "1"; a[n_] := a[n] = Catch[ For[k = a[n-1] + 1, True, k++, If[ StringFreeQ[s, t = ToString[k]], s = s <> t; Throw[k] ] ] ]; Table[a[n], {n, 1, 75}] (* _Jean-François Alcover_, Jan 09 2013 *)
%o (Python) # see Hobson link
%o (Haskell)
%o import Data.List (isInfixOf)
%o a048991 n = a048991_list !! (n-1)
%o a048991_list = f [1..] [] where
%o f (x:xs) ys | xs' `isInfixOf` ys = f xs ys
%o | otherwise = x : f xs (xs' ++ ys)
%o where xs' = reverse $ show x
%o -- _Reinhard Zumkeller_, Dec 05 2011
%o (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
%Y See A048992 for the omitted numbers.
%Y Cf. A105390.
%K nonn,nice,base,easy
%O 1,2
%A _Bernardo Recamán_
%E Edited by _Patrick De Geest_, Jun 02 2003
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