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A271327 Integers k such that the k-th prime divides the product of the first k nonzero Fibonacci numbers.

%I A271327 #24 Jul 24 2019 02:04:14
%S A271327 18,24,29,30,46,47,51,60,63,71,82,89,98,100,102,121,123,127,135,136,
%T A271327 139,145,149,152,156,157,162,163,165,169,180,181,184,185,221,225,235,
%U A271327 251,252,313,316,326,327,329,331,337,359,362,369,399,401,405,428,431,434,436,440,445,448,463
%N A271327 Integers k such that the k-th prime divides the product of the first k nonzero Fibonacci numbers.
%C A271327 Integers k such that A000040(k) divides A003266(k).
%C A271327 If any Fibonacci(j) has a prime divisor p where p is the k-th prime for 1 <= j <= k, then k is a term of this sequence.
%C A271327 There are consecutive pairs such as (29, 30), (46, 47), (135, 136); what is the distribution of such pairs?
%H A271327 Chai Wah Wu, <a href="/A271327/b271327.txt">Table of n, a(n) for n = 1..10000</a>
%e A271327 5 is not a term because A000040(5) = 11 does not appear as a prime divisor of any of the first 5 nonzero Fibonacci numbers.
%e A271327 18 is a term because A003266(18) = 342696507457909818131702784000 is divisible by A000040(18) = 61.
%o A271327 (PARI) lista(nn) = for(n=1, nn, my(p = prime(n)); if (lift(prod(i=1, n, Mod(fibonacci(i), p))) == 0, print1(n, ", ")));
%o A271327 (Python)
%o A271327 from sympy import prime
%o A271327 A271327_list = []
%o A271327 for n in range(1,10**3):
%o A271327     p, a, b = prime(n), 1, 1
%o A271327     for i in range(n):
%o A271327         if not a:
%o A271327             A271327_list.append(n)
%o A271327             break
%o A271327         a, b = b, (a + b) % p # _Chai Wah Wu_, Apr 08 2016
%Y A271327 Cf. A003266, A270653.
%K A271327 nonn
%O A271327 1,1
%A A271327 _Altug Alkan_, Apr 04 2016