

A262283


a(1)=2. For n>1, let s denote the digitstring of a(n1) 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
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OFFSET

1,1


COMMENTS

If a(n1) 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 bfile 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 !! (n1)
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



