A099078 Numbers k such that pi(k).pi(k-1) ... pi(3).pi(2) is prime (dot between numbers means concatenation).

5, 22, 48, 317, 734, 5235, 12377

Offset: 1

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

• base
• more
• nonn

Comments

Number of digits of primes corresponding to the five known terms of this sequence are respectively 4, 21, 67, 605, 1633.

Examples

			5 is in the sequence because pi(5).pi(4).pi(3).pi(2) = 3221 is prime.
		

Links

• Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A046035, A099077, A099079, A099080.

Programs

Maple

r:= 1: v:= 1: Res:= NULL:
for k from 3 to 6000 do
   if isprime(k) then r:= r+1 fi;
   v:= v + r*10^(1+ilog10(v));
   if isprime(v) then Res:= Res, k fi
od:
Res; # Robert Israel, Nov 20 2018

Mathematica

s = ""; Do[s = ToString[PrimePi[n]] <> s; k = ToExpression[s]; If[PrimeQ[k], Print[n]], {n, 2, 5235}] (* Ryan Propper, Aug 30 2005 *)

Extensions

a(6) from Ryan Propper, Aug 30 2005

a(7) from Michael S. Branicky, Apr 29 2023