A125268 Numbers that end with decimal digit 1, 3, 7, or 9 and that produce only composite numbers when any of the digits 0,1,...,9 is inserted anywhere in them (including at the beginning or end).

25011, 52647, 72753, 122313, 168699, 283251, 324021, 598041, 783441, 804131, 837207, 924807, 1247241, 1905759, 2514819, 3461101, 3514077, 3617389, 3905817, 4112913, 4142139, 4203151, 4229871, 4283679, 4531907, 4628827, 4828443, 5380413, 5478091, 5632671, 5714889, 5818569, 5989269, 5990961

Offset: 1

Author

I. J. Kennedy, Jan 15 2007

Keywords

• nonn
• base

Comments

Since digit 0 can be inserted at the beginning of a term, each term must be composite.

Links

• Max Alekseyev, Table of n, a(n) for n = 1..972 (all terms below 10^8)

Crossrefs

Cf. A003459, A124665

Programs

Maple

filter:= proc(n) local x,y,d,t;
  x:= n; y:= 0;
  for d from 0 to ilog10(n)+1 do
     for t from 0 to 9 do
       if isprime(10^(d+1)*x+10^d*t + y) then return false fi;
     od;
     t:= x mod 10;
     y:= y + 10^d*t;
     x:= (x-t)/10;
  od;
  true
end proc:
select(filter, [seq(seq(10*i+j,j=[1,3,7,9]),i=0..10^6)]); # Robert Israel, Sep 12 2016

PARI

{ printA125268(U=8) = my(v,t); v=vector(10^U); forprime(p=11,10^(U+1), if(p<=U,v[p]=p); for(i=1,#Str(p), t=(p\10^i) * 10^(i-1) + (p%10^(i-1)); if(#Str(t)==#Str(p)-1,v[t]=p););); forstep(n=1,10^U,2, if(n%10==5||v[n],next); print1(n,", ");); } \\ prints terms below 10^U, by Max Alekseyev, Sep 12 2016

Extensions

Corrected and extended by Robert G. Wilson v, Jan 26 2007

Removed incorrect terms and extended by Max Alekseyev, Sep 12 2016