A216168 Composite numbers and 1 which yield a prime whenever a 7 is inserted anywhere in them, including at the beginning or end.

1, 9, 27, 33, 39, 57, 87, 159, 177, 187, 603, 717, 753, 949, 1257, 1707, 2277, 2367, 4317, 4623, 4779, 4797, 5773, 6757, 6777, 7017, 7471, 7479, 7747, 7797, 7813, 7977, 8797, 9777, 9987, 10777, 11757, 17679, 28269, 28437, 29779, 34177, 34771, 40059, 41721

Offset: 1

Author

Paolo P. Lava, Sep 03 2012

Keywords

• nonn
• base

Examples

			4623 is not prime but 46237, 46273, 46723, 47623 and 74623 are all primes.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216165-A216167, A216169.

Programs

Magma

[n: n in [1..50000] | not IsPrime(n) and forall{m: t in [0..#Intseq(n)] | IsPrime(m) where m is (Floor(n/10^t)*10+7)*10^t+n mod 10^t}]; // Bruno Berselli, Sep 03 2012

Maple

with(numtheory);
A216168:=proc(q,x)
local a,b,c,i,n,ok;
for n from 1 to q do
if not isprime(n) then
  a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;
  for i from 0 to b do c:=a+9*10^i*trunc(a/10^i)+10^i*x;
    if not isprime(c) then ok:=0; break; fi;
  od;
  if ok=1 then print(n); fi;
fi;
od; end:
A216168(1000,7);