cp's OEIS Frontend

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

%I A099078 #22 Feb 16 2025 08:32:54
%S A099078 5,22,48,317,734,5235,12377
%N A099078 Numbers k such that pi(k).pi(k-1) ... pi(3).pi(2) is prime (dot between numbers means concatenation).
%C A099078 Number of digits of primes corresponding to the five known terms of this sequence are respectively 4, 21, 67, 605, 1633.
%H A099078 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles & Problems connection.
%H A099078 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e A099078 5 is in the sequence because pi(5).pi(4).pi(3).pi(2) = 3221 is prime.
%p A099078 r:= 1: v:= 1: Res:= NULL:
%p A099078 for k from 3 to 6000 do
%p A099078    if isprime(k) then r:= r+1 fi;
%p A099078    v:= v + r*10^(1+ilog10(v));
%p A099078    if isprime(v) then Res:= Res, k fi
%p A099078 od:
%p A099078 Res; # _Robert Israel_, Nov 20 2018
%t A099078 s = ""; Do[s = ToString[PrimePi[n]] <> s; k = ToExpression[s]; If[PrimeQ[k], Print[n]], {n, 2, 5235}] (* _Ryan Propper_, Aug 30 2005 *)
%Y A099078 Cf. A046035, A099077, A099079, A099080.
%K A099078 base,more,nonn
%O A099078 1,1
%A A099078 _Farideh Firoozbakht_, Oct 23 2004
%E A099078 a(6) from _Ryan Propper_, Aug 30 2005
%E A099078 a(7) from _Michael S. Branicky_, Apr 29 2023