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A362376 a(n) is the least k such that Fibonacci(n)*Fibonacci(k) + 1 is a prime, and -1 if no such k exists.

%I A362376 #48 Aug 28 2023 08:21:31
%S A362376 1,1,1,3,3,3,9,3,4,9,3,4,3,27,4,24,24,4,3,6,3,3,444,3,12,9,3,63,6,8,
%T A362376 36,6,36,12,12,4,21,60,4,3,24,73,51,3,11,51,12,4,504,12,3,33,21,6,9,6,
%U A362376 4,384,21,7,54,3,4,51,24,63,30,24,11,45,72,6,39,9,22,42,12,16,60,30
%N A362376 a(n) is the least k such that Fibonacci(n)*Fibonacci(k) + 1 is a prime, and -1 if no such k exists.
%C A362376 The frequencies seem interesting. In the early terms, 5 appears notably rarely, i.e., not until at a(240), whereas several other numbers appear notably frequently, e.g., 24 appears 13 times before a(240). - _Peter Munn_, May 03 2023
%H A362376 Chai Wah Wu, <a href="/A362376/b362376.txt">Table of n, a(n) for n = 1..448</a>
%F A362376 a(n) = A363533(A000045(n)). - _Pontus von Brömssen_, Jun 20 2023
%e A362376 For n=4, Fibonacci(4)=3 and 3*Fibonacci(k)+1 is not prime until k reaches 3, so a(4)=3.
%t A362376 Table[m = Fibonacci[n]; k = 1; While[! PrimeQ[m*Fibonacci[k] + 1], k++]; k, {n, 120}] (* _Michael De Vlieger_, May 03 2023 *)
%o A362376 (PARI) a(n) = my(F=fibonacci(n), k=1); while (!ispseudoprime(F*fibonacci(k) + 1), k++); k; \\ _Michel Marcus_, Apr 18 2023
%o A362376 (Python)
%o A362376 from itertools import count
%o A362376 from sympy import fibonacci, isprime
%o A362376 def A362376(n):
%o A362376     a = b = fibonacci(n)
%o A362376     for k in count(1):
%o A362376         if isprime(a+1):
%o A362376             return k
%o A362376         a, b = b, a+b # _Chai Wah Wu_, May 03 2023
%Y A362376 Cf. A000040, A000045, A034693, A363533.
%K A362376 nonn
%O A362376 1,4
%A A362376 _Jack Braxton_, Apr 17 2023
%E A362376 More terms from _Michel Marcus_, Apr 18 2023