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

Author

N. J. A. Sloane, Sep 18 2015

Keywords

• nonn
• base

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

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..676

Crossrefs

Cf. A080165, A089755, A262282, A262350.

Programs

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

Extensions

More terms from Alois P. Heinz, Sep 18 2015