A030284 a(n) is the least prime > a(n-1) whose digits do not appear in a(n-1).

2, 3, 5, 7, 11, 23, 41, 53, 61, 73, 89, 101, 223, 401, 523, 601, 727, 809, 1117, 2003, 4111, 5003, 6121, 7039, 8111, 9007, 11113, 20029, 31147, 50069, 71143, 80209, 111143, 200009, 311111, 400009, 511111, 600043, 711121, 800053, 911111, 2000003, 4111147, 5000263, 7111199, 8000023, 9111161

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Sequence is infinite. - T. D. Noe, Jun 06 2007

a(n) may never have all of the 4 digits 1, 3, 7, 9: if a(n) has 3 of these digits then a(n+1) ends with the fourth one. - Pierre CAMI, May 06 2011

Links

• T. D. Noe, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A030283, A229364, A000040.

Programs

Haskell

import Data.List (intersect)
a030284 n = a030284_list !! (n-1)
a030284_list = f [] a000040_list where
   f xs (p:ps) = if null $ intersect xs ys then p : f ys ps else f xs ps
                 where ys = show p
-- Reinhard Zumkeller, Sep 21 2013

Mathematica

ta={1};Do[s1=IntegerDigits[Part[ta, Length[ta]]]; s2=IntegerDigits[Prime[n]];If[Equal[Intersection[s1, s2], {}], Print[{Prime[n], Prime[n+1]}];ta=Append[ta, Prime[n]]], {n, 1, 1000000}];ta=Delete[ta, 1] (* Labos Elemer, Nov 18 2004 *)

Extensions

More terms from Labos Elemer, Nov 18 2004