A087368 Prime-indexed primes (PIPs) whose digits are all primes.

3, 5, 277, 353, 773, 3733, 5557, 7523, 7753, 25357, 25733, 27733, 32233, 32323, 32533, 37273, 53233, 53353, 53377, 53777, 55733, 72337, 72727, 73757, 77377, 77557, 232523, 272333, 275773, 322727, 327553, 327757, 333233, 352357, 353527

Offset: 1

Author

Cino Hilliard, Oct 21 2003

Keywords

• easy
• nonn
• base

Comments

Chances are these numbers are infinite since PIPs are infinite.

Examples

			59 is prime, the 59th prime is 277, and 2 and 7 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14683 (terms below 10^11)
• Albert Frank and Philippe Jacqueroux, International Contest, 2001. Item 12.

Crossrefs

Intersection of A006450 and A046034.

Programs

Mathematica

Select[Flatten[Table[FromDigits /@ Tuples[Prime[Range[4]], k], {k, 1, 6}]], PrimeQ[#] && PrimeQ[PrimePi[#]] &] (* Amiram Eldar, Jul 08 2024 *)

PARI

pip(n) = { for(x=1,n, flag=1; y=prime(prime(x)); y2=y; for(j=1,length(Str(y)), r = y%10; if(!isprime(r),flag=0); y = floor(y/10); ); if(flag,print1(y2",")); ) }

Extensions

Offset corrected by Amiram Eldar, Jul 08 2024