

A346063


a(n) = primepi(A039634(prime(n)^21)).


3



2, 1, 2, 2, 4, 3, 1, 5, 1, 6, 4, 3, 6, 4, 7, 14, 6, 10, 7, 37, 23, 25, 28, 18, 21, 22, 67, 24, 9, 46, 11, 19, 62, 12, 40, 24, 2, 27, 6, 91, 11, 31, 20, 1, 36, 203, 69, 25, 2, 80, 16, 48, 155, 18, 1, 326, 7, 20, 109, 365, 8, 39, 9, 240, 438, 2, 16, 154, 10, 17
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OFFSET

1,1


COMMENTS

This sequence looks at the effect on p^2  1 of A039634 with the primes represented by their indices. It seems that primes obtained by iterating the map A039634 on p^2  1 never fall into a cycle before reaching 2. Conjecture: Iterating the map k > a(k) eventually reaches 1. For example, 1 > 2 > 1; 5 > 4 > 2 > 1; and 27 > 67 > 16 > 14 > 4 > 2 > 1.
If the conjecture holds, then A339991(n) != 1 and A340419 is a finite sequence.


LINKS



FORMULA



MATHEMATICA

Array[PrimePi@ FixedPoint[If[EvenQ[#] && # > 2, #/2, If[PrimeQ[#]  (# === 1), #, (#  1)/2]] &, Prime[#]^2  1] &, 70] (* Michael De Vlieger, Jul 06 2021 *)


PROG

(Python)
from sympy import prime, isprime, primepi
def a(n):
p = prime(n); m = p*p  1
while not isprime(m): m = m//2
return primepi(m)
for n in range(1, 71): print(a(n))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



