A270653 -id:A270653 - cp's OEIS frontend

A270777 Integers k such that A003266(k) is not divisible by k.

2, 3, 4, 7, 23, 43, 67, 83, 103, 127, 163, 167, 223, 227, 283, 367, 383, 443, 463, 467, 487, 503, 523, 547, 587, 607, 643, 647, 683, 727, 787, 823, 827, 863, 883, 887, 907, 947, 983, 1063, 1123, 1163, 1187, 1283, 1303, 1327, 1367, 1423, 1447, 1487, 1543, 1567, 1583, 1607, 1627, 1663, 1667

Offset: 1

Altug Alkan, Mar 22 2016

nonn

			4 is a term because 1*1*2*3 = 6 is not divisible by 4.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Complement of A270653.

Cf. A000057, A003266.

Select[Range@ 1680, ! Divisible[Fibonorial@ #, #] &] (* Version 10, or *)
Select[Range@ 1680, ! Divisible[Product[Fibonacci@ k, {k, #}], #] &] (* Michael De Vlieger, Mar 27 2016 *)

t(n) = prod(k=1, n, Mod(fibonacci(k), n));
for(n=1, 2000, if(lift(t(n)) != 0, print1(n, ", ")));

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

Original entry on oeis.org

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

Altug Alkan, Apr 04 2016

nonn

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?

			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.

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

Cf. A003266, A270653.

lista(nn) = for(n=1, nn, my(p = prime(n)); if (lift(prod(i=1, n, Mod(fibonacci(i), p))) == 0, print1(n, ", ")));

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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A270777 Integers k such that A003266(k) is not divisible by k.

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