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A271327 Integers k such that the k-th prime divides the product of the first k nonzero Fibonacci numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 12:36 EST 2023. Contains 360116 sequences. (Running on oeis4.)