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

%I A333364 #16 Sep 14 2022 07:27:06
%S A333364 2,3,7,11,13,17,19,23,29,37,41,43,47,53,61,67,71,73,79,83,89,97,101,
%T A333364 103,107,109,113,127,131,137,139,149,151,157,163,167,173,181,191,193,
%U A333364 197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283
%N A333364 Indices of primes p whose order of primeness A078442(p) is prime.
%C A333364 All terms are prime.
%H A333364 Alois P. Heinz, <a href="/A333364/b333364.txt">Table of n, a(n) for n = 1..10000</a>
%H A333364 N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>
%H A333364 N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]
%F A333364 { p in primes : A049076(p) is prime }.
%F A333364 a(n) = pi(A333353(n)), with pi = A000720.
%e A333364 11 is a term: prime(11) = 31 -> 11 -> 5 -> 3 -> 2 -> 1, five (a prime number of) steps "->" = pi = A000720.
%p A333364 b:= proc(n) option remember;
%p A333364       `if`(isprime(n), 1+b(numtheory[pi](n)), 0)
%p A333364     end:
%p A333364 a:= proc(n) option remember; local p;
%p A333364       p:= `if`(n=1, 1, a(n-1));
%p A333364       do p:= nextprime(p);
%p A333364          if isprime(b(p)+1) then break fi
%p A333364       od; p
%p A333364     end:
%p A333364 seq(a(n), n=1..62);
%t A333364 b[n_] := b[n] = If[PrimeQ[n], 1 + b[PrimePi[n]], 0];
%t A333364 a[n_] := a[n] = Module[{p}, p = If[n == 1, 1, a[n - 1]];
%t A333364    While[True, p = NextPrime[p]; If[PrimeQ[b[p] + 1], Break[]]]; p];
%t A333364 Table[a[n], {n, 1, 62}] (* _Jean-François Alcover_, Sep 14 2022, after _Alois P. Heinz_ *)
%Y A333364 Cf. A000040, A000720, A049076, A333353.
%K A333364 nonn
%O A333364 1,1
%A A333364 _Alois P. Heinz_, Mar 16 2020