A362376 - OEIS

%I #48 Aug 28 2023 08:21:31

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

%C 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 Chai Wah Wu, <a href="/A362376/b362376.txt">Table of n, a(n) for n = 1..448</a>

%F a(n) = A363533(A000045(n)). - _Pontus von Brömssen_, Jun 20 2023

%e For n=4, Fibonacci(4)=3 and 3*Fibonacci(k)+1 is not prime until k reaches 3, so a(4)=3.

%t Table[m = Fibonacci[n]; k = 1; While[! PrimeQ[m*Fibonacci[k] + 1], k++]; k, {n, 120}] (* _Michael De Vlieger_, May 03 2023 *)

%o (PARI) a(n) = my(F=fibonacci(n), k=1); while (!ispseudoprime(F*fibonacci(k) + 1), k++); k; \\ _Michel Marcus_, Apr 18 2023

%o (Python)

%o from itertools import count

%o from sympy import fibonacci, isprime

%o def A362376(n):

%o     a = b = fibonacci(n)

%o     for k in count(1):

%o         if isprime(a+1):

%o             return k

%o         a, b = b, a+b # _Chai Wah Wu_, May 03 2023

%Y Cf. A000040, A000045, A034693, A363533.

%K nonn

%O 1,4

%A _Jack Braxton_, Apr 17 2023

%E More terms from _Michel Marcus_, Apr 18 2023