cp's OEIS Frontend

A346063 a(n) = primepi(A039634(prime(n)^2-1)).

%I A346063 #29 Aug 08 2021 11:27:39
%S A346063 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,
%T A346063 46,11,19,62,12,40,24,2,27,6,91,11,31,20,1,36,203,69,25,2,80,16,48,
%U A346063 155,18,1,326,7,20,109,365,8,39,9,240,438,2,16,154,10,17
%N A346063 a(n) = primepi(A039634(prime(n)^2-1)).
%C A346063 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.
%C A346063 If the conjecture holds, then A339991(n) != -1 and A340419 is a finite sequence.
%H A346063 Ya-Ping Lu, <a href="/A346063/a346063.pdf">Plot of a(n) vs n for n up to 10000</a>
%F A346063 a(n) = A000720(A039634(A000040(n)^2-1)). - _Pontus von Brömssen_, Jul 03 2021
%t A346063 Array[PrimePi@ FixedPoint[If[EvenQ[#] && # > 2, #/2, If[PrimeQ[#] || (# === 1), #, (# - 1)/2]] &, Prime[#]^2 - 1] &, 70] (* _Michael De Vlieger_, Jul 06 2021 *)
%o A346063 (Python)
%o A346063 from sympy import prime, isprime, primepi
%o A346063 def a(n):
%o A346063     p = prime(n); m = p*p - 1
%o A346063     while not isprime(m): m = m//2
%o A346063     return primepi(m)
%o A346063 for n in range(1, 71): print(a(n))
%Y A346063 Cf. A000040, A000720, A039634, A339991, A340008, A340418, A340419.
%K A346063 nonn
%O A346063 1,1
%A A346063 _Ya-Ping Lu_, Jul 03 2021