A217045 - OEIS

%I #14 Dec 04 2017 19:11:34

%S 19,37,43,61,67,73,97,109,199,211,223,241,349,409,421,457,463,541,571,

%T 751,757,823,991,1033,1087,1321,1423,1447,1543,2749,3361,3469,3499,

%U 3847,4111,4273,4483,5059,5437,5443,5449,6373,6709,6793,7687,8089,8221,8443

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

%H Paolo P. Lava, <a href="/A217045/b217045.txt">Table of n, a(n) for n = 1..141</a>

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

%p with(numtheory);

%p A217045:=proc(q,x)

%p local a,b,c,i,n,ok;

%p for n from 5 to q do

%p a:=ithprime(n); b:=0;

%p while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;

%p   for i from 1 to b-1 do

%p     c:=a+9*10^i*trunc(a/10^i)+10^i*x;

%p     if not isprime(c) then ok:=0; break; fi; od;

%p   if ok=1 then print(ithprime(n)); fi;

%p od; end:

%p A217045(100000,4)

%t 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 *)

%o (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

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

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Sep 25 2012