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A215417 Primes that remain prime when a single zero digit is inserted between any two adjacent digits.

%I A215417 #31 May 21 2018 03:30:03
%S A215417 11,13,17,19,37,41,53,59,61,67,71,79,89,97,109,113,131,149,191,197,
%T A215417 227,239,269,281,283,337,367,379,383,401,421,449,457,499,503,509,587,
%U A215417 607,673,701,719,727,739,757,809,811,887,907,929,991,1009,1061,1093,1103
%N A215417 Primes that remain prime when a single zero digit is inserted between any two adjacent digits.
%H A215417 Giovanni Resta, <a href="/A215417/b215417.txt">Table of n, a(n) for n = 1..4300</a> (terms a(1)-a(372) from Paolo P. Lava, terms a(373)-a(700) from Vincenzo Librandi)
%e A215417 399617 is prime and also 3996107, 3996017, 3990617, 3909617, 3099617.
%p A215417 A215417:=proc(q)
%p A215417 local a,b,c,i,n,ok;
%p A215417 for n from 5 to q do
%p A215417   a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
%p A215417   a:=ithprime(n);ok:=1;
%p A215417   for i from 1 to b-1 do
%p A215417     c:=a+9*10^i*trunc(a/10^i); if not isprime(c) then ok:=0; break; fi;
%p A215417   od;
%p A215417   if ok=1 then print(ithprime(n)); fi;
%p A215417 od; end:
%p A215417 A215417(1000);
%t A215417 Select[Prime[Range[5,200]],And@@PrimeQ[Table[FromDigits[Insert[ IntegerDigits[ #],0,n]],{n,2,IntegerLength[#]}]]&] (* _Harvey P. Dale_, Feb 23 2014 *)
%o A215417 (PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=0; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A215417 Cf. A159236, A069246, A215419-A215421.
%K A215417 nonn,base
%O A215417 1,1
%A A215417 _Paolo P. Lava_, Aug 10 2012