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

1,1

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)

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

Prog

(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

Crossrefs

Cf. A003459, A124665

Sequence in context: A252846 A031651 A263815 * A212726 A258542 A205041

Adjacent sequences: A125265 A125266 A125267 * A125269 A125270 A125271

Keyword

nonn,base

Author

I. J. Kennedy, Jan 15 2007

Extensions

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

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

Status

approved