A333353 Primes p whose order of primeness A078442(p) is prime.

3, 5, 17, 31, 41, 59, 67, 83, 109, 157, 179, 191, 211, 241, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471, 1499, 1523, 1597, 1621

Offset: 1

Author

Alois P. Heinz, Mar 15 2020

Keywords

• nonn

Examples

			31 is a term: 31 -> 11 -> 5 -> 3 -> 2 -> 1, five (a prime number of) steps "->" = pi = A000720.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• N. Fernandez, An order of primeness, F(p)
• N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Crossrefs

Cf. A000040, A000720, A049076, A078442, A236542, A262275, A333364.

Programs

Maple

b:= proc(n) option remember;
      `if`(isprime(n), 1+b(numtheory[pi](n)), 0)
    end:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if isprime(b(p)) then break fi
      od; p
    end:
seq(a(n), n=1..55);

Mathematica

b[n_] := b[n] = If[!PrimeQ[n], 0, 1+b[PrimePi[n]]];
okQ[n_] := PrimeQ[n] && PrimeQ[b[n]];
Select[Range[2000], okQ] (* Jean-François Alcover, May 30 2022 *)

Formula

{ p in primes : A078442(p) is prime }.

a(n) = prime(A333364(n)).