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 A346063 a(n) = primepi(A039634(prime(n)^2-1)). 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..70. Ya-Ping Lu, Plot of a(n) vs n for n up to 10000 FORMULA a(n) = A000720(A039634(A000040(n)^2-1)). - Pontus von Brömssen, Jul 03 2021 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 Cf. A000040, A000720, A039634, A339991, A340008, A340418, A340419. Sequence in context: A020475 A156995 A131183 * A133770 A288310 A332718 Adjacent sequences: A346060 A346061 A346062 * A346064 A346065 A346066 KEYWORD nonn AUTHOR Ya-Ping Lu, Jul 03 2021 STATUS approved

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Last modified August 7 08:03 EDT 2024. Contains 375008 sequences. (Running on oeis4.)