A193733 Start of n consecutive indices k such that Fibonacci(k) contains distinct number of divisors.

1, 2, 10, 12, 20, 20, 54, 96, 132, 171, 222, 458, 520, 731, 1083

Offset

1,2

Comments

a(16) > 1443, if it exists. - Chai Wah Wu, Jan 19 2020

Links

Table of n, a(n) for n=1..15.

Example

The 4th number of this sequence, 12, means that:
Fibonacci(12) = 144 = 2 ^ 4 * 3 ^ 2,
Fibonacci(13) = 233 (prime number),
Fibonacci(14) = 377 = 13 * 29,
Fibonacci(15) = 610 = 2 * 5 * 61,
and these Fibonacci numbers have distinct number of divisors: 15, 2, 4 and 8, respectively.

Maple

with(combinat, fibonacci):with(numtheory): for n from 1 to 10 do: i:=0:for k from 1 to 1500 while(i=0) do: lst:={}:for p from 0 to n-1 do :x:= fibonacci(k+p):y:=divisors(x):n1:=nops(y):lst:= lst union {n1}:od:if nops(lst)=n then  printf(`%d, `, k): i:=1:else fi:od:od:

Crossrefs

Cf. A000045, A063375.

Sequence in context: A374182 A374181 A178504 * A167503 A130842 A061818

Adjacent sequences: A193730 A193731 A193732 * A193734 A193735 A193736

Keyword

nonn,hard,more

Author

Michel Lagneau, Aug 08 2011

Extensions

a(12)-a(15) from Amiram Eldar, Oct 18 2019

Status

approved