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 A262283 a(1)=2. For n>1, let s denote the digit-string of a(n-1) with the first digit omitted. Then a(n) is the smallest prime not yet present which starts with s. 6
 2, 3, 5, 7, 11, 13, 31, 17, 71, 19, 97, 73, 37, 79, 907, 701, 101, 103, 307, 709, 911, 113, 131, 311, 1103, 1031, 313, 137, 373, 733, 331, 317, 173, 739, 397, 971, 719, 191, 919, 193, 937, 379, 797, 977, 773, 7307, 3079, 7901, 9011, 1109, 109, 929, 29, 941, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If a(n-1) has a single digit then a(n) is simply the smallest missing prime. Leading zeros in s are ignored. The sequence is infinite, since there infinitely many primes that start with s (see the comments in A080165). The data in the b-file suggests that there are infinitely many primes that do not appear. Hoever, at present that is no proof that even one prime (23, say) never appears. - N. J. A. Sloane, Sep 20 2015 Alois P. Heinz points out that a(n) = A262282(n+29) starting at the 103rd term. - N. J. A. Sloane, Sep 19 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..676 EXAMPLE a(1)=2, so s is the empty string, so a(2) is the smallest missing prime, 3. After a(6)=13, s=3, so a(7) is the smallest missing prime that starts with 3, which is 31. PROG (Haskell) import Data.List (isPrefixOf, delete) a262283 n = a262283_list !! (n-1) a262283_list = 2 : f "" (map show \$ tail a000040_list) where    f xs pss = (read ys :: Integer) :               f (dropWhile (== '0') ys') (delete ys pss)               where ys@(_:ys') = head \$ filter (isPrefixOf xs) pss -- Reinhard Zumkeller, Sep 19 2015 CROSSREFS Cf. A080165, A089755, A262282, A262350. Sequence in context: A067908 A236128 A332341 * A187614 A191077 A262377 Adjacent sequences:  A262280 A262281 A262282 * A262284 A262285 A262286 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Sep 18 2015 EXTENSIONS More terms from Alois P. Heinz, Sep 18 2015 STATUS approved

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Last modified May 5 19:23 EDT 2021. Contains 343573 sequences. (Running on oeis4.)