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.

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

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