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A333364
Indices of primes p whose order of primeness A078442(p) is prime.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 16 2020
STATUS
approved