A089770 - OEIS

%I #10 Dec 11 2017 02:45:38

%S 2,11,101,1009,10009,100049,1000081,10000169,100000049,1000000009,

%T 10000000069,100000000069,1000000000091,10000000000099,

%U 100000000000099,1000000000000091,10000000000000069,100000000000000049

%N Smallest n-digit prime containing no prime substrings, or 0 if no such number exists.

%C For n > 1, a(n) ends in 1 or 9 while other digits can be 0,1,4,6,8 or 9. - _Robert Israel_, Dec 09 2017

%H Robert Israel, <a href="/A089770/b089770.txt">Table of n, a(n) for n = 1..999</a>

%e a(3) = 149 is a term as 1,4,9,14,49 are all nonprimes. 199 is not a member as 19 is a prime.

%p N:= 1000: # to get terms until the first where a(n) > 10^(n-1)+10*N+9

%p filter1:= proc(x)

%p   local k,j;

%p   for k from 0 to ilog10(x) do

%p      for j from k to ilog10(x)+1 do

%p        if isprime(floor((x mod 10^j)/10^k)) then return false fi;

%p   od od:

%p   true

%p end proc:

%p X:= select(filter1, [seq(seq(10*i+j,j=[1,9]),i=0..N)]):

%p filter2:= proc(p,x)

%p     local k,j;

%p     if not isprime(p) then return false fi;

%p     for k from 1 to ilog10(x)+1 do

%p      if isprime(floor(p /10^k)) then return false fi

%p     od;

%p     true;

%p end proc:

%p for n from 1 do

%p found:= false;

%p for x in X do

%p     p:= 10^(n-1)+x;

%p     if filter2(p,x) then A[n]:= p; found:= true; break fi;

%p od:

%p if not found then break fi

%p od:

%p seq(A[i],i=1..n-1); # _Robert Israel_, Dec 09 2017

%Y Cf. A089768, A033274, A089771.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 23 2003

%E Corrected and extended by _David Wasserman_, Oct 12 2005