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 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 (list; graph; refs; listen; history; text; internal format)
 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 n-digit terms as (9, 53, 339, 2552, ...). - M. F. Hasler, Oct 25 2019 REFERENCES Invented by 10-year-old 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[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 *) PROG (Python) # see Hobson link (Haskell) import Data.List (isInfixOf) a048991 n = a048991_list !! (n-1) 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 EXTENSIONS Edited by Patrick De Geest, Jun 02 2003 STATUS approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)