A217045 Primes that remain prime when a single "4" digit is inserted between any two adjacent decimal digits.

19, 37, 43, 61, 67, 73, 97, 109, 199, 211, 223, 241, 349, 409, 421, 457, 463, 541, 571, 751, 757, 823, 991, 1033, 1087, 1321, 1423, 1447, 1543, 2749, 3361, 3469, 3499, 3847, 4111, 4273, 4483, 5059, 5437, 5443, 5449, 6373, 6709, 6793, 7687, 8089, 8221, 8443

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..141

Example

87697 is prime and also 876947, 876497, 874697 and 847697.

Maple

with(numtheory);
A217045:=proc(q, x)
local a, b, c, i, n, ok;
for n from 5 to q do
a:=ithprime(n); b:=0;
while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;
  for i from 1 to b-1 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(ithprime(n)); fi;
od; end:
A217045(100000, 4)

Mathematica

Select[Prime[Range[5, 1500]], AllTrue[Table[FromDigits[Insert[ IntegerDigits[ #], 4, n]], {n, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 04 2017 *)

Prog

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=4; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044, A217046, A217047, A217062-A217065

Sequence in context: A354431 A059695 A134196 * A139313 A272205 A347371

Adjacent sequences: A217042 A217043 A217044 * A217046 A217047 A217048

Keyword

nonn,base

Author

Paolo P. Lava, Sep 25 2012

Status

approved