A216165 Composite numbers and 1 which yield a prime whenever a 1 is inserted anywhere in them, including at the beginning or end.

1, 49, 63, 81, 91, 99, 117, 123, 213, 231, 279, 319, 427, 459, 621, 697, 721, 801, 951, 987, 1113, 1131, 1261, 1821, 1939, 2101, 2149, 2211, 2517, 2611, 3151, 3219, 4011, 4411, 4887, 5031, 5361, 6231, 6487, 7011, 7209, 8671, 9141, 9801, 10051, 10161, 10281

Offset

1,2

Links

Paolo P. Lava, Table of n, a(n) for n = 1..250

Example

7209 is not prime but 72091, 72019, 72109, 71209 and 17209 are all primes.

Maple

with(numtheory);
A216165:=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:
A216165(1000, 1);

Mathematica

Join[{1}, Select[Range[11000], CompositeQ[#]&&AllTrue[FromDigits/@ Table[ Insert[ IntegerDigits[#], 1, i], {i, IntegerLength[#]+1}], PrimeQ]&]] (* Harvey P. Dale, Mar 24 2017 *) (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 24 2017 *)

Prog

(Magma) [n: n in [1..11000] | not IsPrime(n) and forall{m: t in [0..#Intseq(n)] | IsPrime(m) where m is (Floor(n/10^t)*10+1)*10^t+n mod 10^t}]; // Bruno Berselli, Sep 03 2012

Crossrefs

Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216166-A216169.

Sequence in context: A202001 A038640 A326151 * A374937 A065807 A038678

Adjacent sequences: A216162 A216163 A216164 * A216166 A216167 A216168

Keyword

nonn,base

Author

Paolo P. Lava, Sep 03 2012

Status

approved