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

1,1

Comments

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

Links

Table of n, a(n) for n=1..7.

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Example

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

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 *)

Crossrefs

Cf. A046035, A099077, A099079, A099080.

Sequence in context: A082005 A273024 A273121 * A272836 A273575 A272848

Adjacent sequences: A099075 A099076 A099077 * A099079 A099080 A099081

Keyword

base,more,nonn

Author

Farideh Firoozbakht, Oct 23 2004

Extensions

a(6) from Ryan Propper, Aug 30 2005

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

Status

approved