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

1,1

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 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

Links

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

Example

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.

Prog

(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

Crossrefs

Suggested by A089755. Cf. A262283.

Cf. A262356.

Sequence in context: A022481 A156338 A272817 * A034080 A107805 A177378

Adjacent sequences: A262279 A262280 A262281 * A262283 A262284 A262285

Keyword

nonn,base

Author

Franklin T. Adams-Watters and N. J. A. Sloane, Sep 18 2015

Extensions

More terms from Alois P. Heinz, Sep 18 2015

Status

approved