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

1,1

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]

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A079496 A230639 A038898 * A297175 A089133 A103149

Adjacent sequences: A333350 A333351 A333352 * A333354 A333355 A333356

Keyword

nonn

Author

Alois P. Heinz, Mar 15 2020

Status

approved