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

18, 24, 29, 30, 46, 47, 51, 60, 63, 71, 82, 89, 98, 100, 102, 121, 123, 127, 135, 136, 139, 145, 149, 152, 156, 157, 162, 163, 165, 169, 180, 181, 184, 185, 221, 225, 235, 251, 252, 313, 316, 326, 327, 329, 331, 337, 359, 362, 369, 399, 401, 405, 428, 431, 434, 436, 440, 445, 448, 463

Offset

1,1

Comments

Integers k such that A000040(k) divides A003266(k).

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.

There are consecutive pairs such as (29, 30), (46, 47), (135, 136); what is the distribution of such pairs?

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

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.
18 is a term because A003266(18) = 342696507457909818131702784000 is divisible by A000040(18) = 61.

Prog

(PARI) lista(nn) = for(n=1, nn, my(p = prime(n)); if (lift(prod(i=1, n, Mod(fibonacci(i), p))) == 0, print1(n, ", ")));
(Python)
from sympy import prime
A271327_list = []
for n in range(1, 10**3):
    p, a, b = prime(n), 1, 1
    for i in range(n):
        if not a:
            A271327_list.append(n)
            break
        a, b = b, (a + b) % p # Chai Wah Wu, Apr 08 2016

Crossrefs

Cf. A003266, A270653.

Sequence in context: A182438 A050772 A086473 * A243539 A076770 A105679

Adjacent sequences: A271324 A271325 A271326 * A271328 A271329 A271330

Keyword

nonn

Author

Altug Alkan, Apr 04 2016

Status

approved