A216166 Composite numbers and 1 which yield a prime whenever a 3 is inserted anywhere in them (including at the beginning or end).

1, 121, 343, 361, 533, 637, 793, 889, 943, 1183, 3013, 3223, 3353, 3403, 3757, 3827, 3893, 4313, 4543, 4963, 8653, 10423, 14257, 20339, 23083, 23419, 30917, 33031, 33101, 33323, 33433, 33701, 33821, 34333, 34393, 35453, 36437, 36533, 39137, 39247, 42869, 43337

Offset

1,2

Links

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

Example

3827 is not prime but 38273, 38237, 38327 and 33827 are all primes.

Maple

with(numtheory);
A216166:=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:
A216166(1000, 3);

Mathematica

ap3Q[n_]:=CompositeQ[n]&&AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ n], 3, k], {k, IntegerLength[n]+1}], PrimeQ]; Join[{1}, Select[Range[ 44000], ap3Q]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 25 2020 *)

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+3)*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: A112075 A068872 A203856 * A208242 A167721 A330670

Adjacent sequences: A216163 A216164 A216165 * A216167 A216168 A216169

Keyword

nonn,base

Author

Paolo P. Lava, Sep 03 2012

Status

approved