A089770 Smallest n-digit prime containing no prime substrings, or 0 if no such number exists.

2, 11, 101, 1009, 10009, 100049, 1000081, 10000169, 100000049, 1000000009, 10000000069, 100000000069, 1000000000091, 10000000000099, 100000000000099, 1000000000000091, 10000000000000069, 100000000000000049

Offset: 1

Author

Amarnath Murthy, Nov 23 2003

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A089768, A033274, A089771.

Programs

Maple

N:= 1000: # to get terms until the first where a(n) > 10^(n-1)+10*N+9
filter1:= proc(x)
  local k,j;
  for k from 0 to ilog10(x) do
     for j from k to ilog10(x)+1 do
       if isprime(floor((x mod 10^j)/10^k)) then return false fi;
  od od:
  true
end proc:
X:= select(filter1, [seq(seq(10*i+j,j=[1,9]),i=0..N)]):
filter2:= proc(p,x)
    local k,j;
    if not isprime(p) then return false fi;
    for k from 1 to ilog10(x)+1 do
     if isprime(floor(p /10^k)) then return false fi
    od;
    true;
end proc:
for n from 1 do
found:= false;
for x in X do
    p:= 10^(n-1)+x;
    if filter2(p,x) then A[n]:= p; found:= true; break fi;
od:
if not found then break fi
od:
seq(A[i],i=1..n-1); # Robert Israel, Dec 09 2017

Extensions

Corrected and extended by David Wasserman, Oct 12 2005