A333364 Indices of primes p whose order of primeness A078442(p) is prime.

2, 3, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283

Offset

1,1

Comments

All terms are prime.

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 : A049076(p) is prime }.

a(n) = pi(A333353(n)), with pi = A000720.

Example

11 is a term: prime(11) = 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)+1) then break fi
      od; p
    end:
seq(a(n), n=1..62);

Mathematica

b[n_] := b[n] = If[PrimeQ[n], 1 + b[PrimePi[n]], 0];
a[n_] := a[n] = Module[{p}, p = If[n == 1, 1, a[n - 1]];
   While[True, p = NextPrime[p]; If[PrimeQ[b[p] + 1], Break[]]]; p];
Table[a[n], {n, 1, 62}] (* Jean-François Alcover, Sep 14 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A000720, A049076, A333353.

Sequence in context: A020634 A173555 A086339 * A332787 A181173 A216277

Adjacent sequences: A333361 A333362 A333363 * A333365 A333366 A333367

Keyword

nonn

Author

Alois P. Heinz, Mar 16 2020

Status

approved