%I
%S 11,13,3,2,5,7,17,71,19,97,73,31,101,103,37,79,907,701,107,709,911,
%T 113,131,311,1103,1031,313,137,373,733,331,317,173,739,397,971,719,
%U 191,919,193,937,379,797,977,773,7307,307,727,271,7103,1033,337,3701,7013
%N a(1)=11. 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.
%C If a(n1) has a single digit then a(n) is simply the smallest missing prime.
%C Leading zeros in s are ignored.
%C The bfile 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.
%C _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
%C A variant without the prime number condition: A262356.  _Reinhard Zumkeller_, Sep 19 2015
%H Alois P. Heinz, <a href="/A262282/b262282.txt">Table of n, a(n) for n = 1..705</a>
%e 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.
%o (Haskell)
%o import Data.List (isPrefixOf, delete)
%o a262282 n = a262282_list !! (n1)
%o a262282_list = 11 : f "1" (map show (delete 11 a000040_list)) where
%o f xs pss = (read ys :: Integer) :
%o f (dropWhile (== '0') ys') (delete ys pss)
%o where ys@(_:ys') = head $ filter (isPrefixOf xs) pss
%o  _Reinhard Zumkeller_, Sep 19 2015
%Y Suggested by A089755. Cf. A262283.
%Y Cf. A262356.
%K nonn,base
%O 1,1
%A _Franklin T. AdamsWatters_ and _N. J. A. Sloane_, Sep 18 2015
%E More terms from _Alois P. Heinz_, Sep 18 2015
