A099079 -id:A099079 - cp's OEIS frontend

A099077 Numbers k such that pi(1).pi(2) ... pi(k-1).pi(k) is prime (dot between numbers means concatenation).

5, 25, 2232, 4560

Offset: 1

Farideh Firoozbakht, Oct 23 2004

Number of digits of primes corresponding to the four known terms of this sequence are respectively 4,24,6127,13111. Next term is greater than 10250 and the prime corresponding to the next term has more than 32500 digits.

a(5) > 35000. - Michael S. Branicky, Nov 25 2024

			5 is in the sequence because pi(1).pi(2).pi(3).pi(4).pi(5)=1223 is prime.

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

Cf. A000720, A046035, A099078, A099079, A099080.

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

Original entry on oeis.org

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

Offset: 1

Farideh Firoozbakht, Oct 23 2004

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

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

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

Cf. A046035, A099077, A099079, A099080.

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

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

a(6) from Ryan Propper, Aug 30 2005

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

A099080 Numbers k such that sigma(k).sigma(k-1) ... sigma(2).sigma(1) is prime (dot between numbers means concatenation).

Original entry on oeis.org

2, 3, 66, 102

Offset: 1

Farideh Firoozbakht, Oct 23 2004

Numbers of digits of primes corresponding to the four known terms of this sequence are respectively 2, 3, 133, and 232.
A naive heuristic suggests that this sequence is infinite but extremely sparse. - Charles R Greathouse IV, Nov 05 2013
There are no more terms below 10000. - Charles R Greathouse IV, Nov 09 2013
There are no more terms below 20000. - Michael S. Branicky, Nov 25 2024

			3 is in the sequence because sigma(3).sigma(2).sigma(1) = 431 is prime.

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

Cf. A046035, A099077, A099078, A099079.

Module[{nn=110,d},d=DivisorSigma[1,Range[nn]];Select[Range[nn], PrimeQ[ FromDigits[ Flatten[IntegerDigits/@Reverse[Take[d,#]]]]]&]] (* Harvey P. Dale, Jul 25 2016 *)

s="1";for(n=2,1e3,s=Str(sigma(n),s);if(ispseudoprime(eval(s)), print1(n", "))) \\ Charles R Greathouse IV, Nov 05 2013

cp's OEIS Frontend

A099077 Numbers k such that pi(1).pi(2) ... pi(k-1).pi(k) is prime (dot between numbers means concatenation).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A099080 Numbers k such that sigma(k).sigma(k-1) ... sigma(2).sigma(1) is prime (dot between numbers means concatenation).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI