A262282 a(1)=11. 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.

11, 13, 3, 2, 5, 7, 17, 71, 19, 97, 73, 31, 101, 103, 37, 79, 907, 701, 107, 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, 307, 727, 271, 7103, 1033, 337, 3701, 7013

Offset: 1

Author

Franklin T. Adams-Watters and 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 b-file suggests that there are infinitely many primes that do not appear in the sequence. However, there is no proof at present that any particular prime (23, say) never appears.

Alois P. Heinz points out that this sequence and A262283 eventually merge (see the latter entry for details). - N. J. A. Sloane, Sep 19 2015

A variant without the prime number condition: A262356. - Reinhard Zumkeller, Sep 19 2015

Examples

			a(1)=11, so s=1, a(2) is smallest missing prime that starts with 1, so a(2)=13. Then s=3, so a(3)=3. Then s is the empty string, so a(4)=2, and so on.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..705

Crossrefs

Suggested by A089755. Cf. A262283.

Cf. A262356.

Programs

Haskell

import Data.List (isPrefixOf, delete)
a262282 n = a262282_list !! (n-1)
a262282_list = 11 : f "1" (map show (delete 11 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