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

1,2

Links

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

Example

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

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);

Prog

(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

Crossrefs

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

Sequence in context: A255343 A108107 A340237 * A036303 A359030 A325299

Adjacent sequences: A216165 A216166 A216167 * A216169 A216170 A216171

Keyword

nonn,base

Author

Paolo P. Lava, Sep 03 2012

Status

approved