[seqfan] Re: A001576

[f.firoozbakht at sci.ui.ac.ir]

> Are there other  n (besides 1,3,9)   such as
> 1 +2^n+4^n is prime ?

   Number of digits of a(n)=(2^3^(n+1)-1)/(2^3^n-1)=1+2^(3^n)+4^(3^n)
for n=0,1,...,10 are 1,2,6,17,49,147,439,1317,3951,11851,35552.
Between the first 11 terms of the sequence {a(n)} (A051154) only for
n<3, a(n) is prime and for n>10 a(n) has more than 106000 digits.


---Farideh


Quoting Jacques Tramu <jacques.tramu at echolalie.com>:

> Are there other  n (besides 1,3,9)   such as
> 1 +2^n+4^n is prime ?
>
>> From: <vincenzo.librandi at tin.it>
>> Conjecture
>> If a(n) =1^n+2^n+4^n= prime number,
>>   then
>>   n is the
>> form
>>   3^h.
>>
>> Example:
>>   For h=1, n=3, and 1^3+2^3+4^3=73 (prime)
>>
>> h=2, n=9,
>> and
>>   1^9+2^9+4^9=262657 (prime)
>
>
>
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