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A271327
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Integers k such that the k-th prime divides the product of the first k nonzero Fibonacci numbers.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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?
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..10000
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A003266, A270653.
Sequence in context: A182438 A050772 A086473 * A243539 A076770 A105679
Adjacent sequences: A271324 A271325 A271326 * A271328 A271329 A271330
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KEYWORD
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nonn
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AUTHOR
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Altug Alkan, Apr 04 2016
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STATUS
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approved
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