# What should I name this sequence?

I have found a new sequence of primes that is generated by

$3^n - 2$

The sequence is

$7, 79, 241, 727, 19681, 31381059607, 450283905890997361, 36472996377170786401, 8727963568067712425891397479476727340041447, 4638397686588101979328150167890591454318967698007, 125236737537878753441860054533045969266612127846241$

so far.

The highest I have got is

$3^{193} - 2$

This is an ongoing project.

Just help me name the sequence.

Note: For those who want to help me: Alpertron Integer Factorization Calculator

Note by Yajat Shamji
6 months, 1 week ago

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Sort by:

- 6 months, 1 week ago

@Yajat Shamji Suggested name : Yajat primes ?

- 6 months, 1 week ago

I would like a flair of imagination - I don't want my name associated with this:

'A true mathematician will never associate himself with a finding - he will always associate his partners, showing selflessness whilst glorifying his partners - that's the ultimate sacrifice and that defines a true mathematician.'

- 6 months, 1 week ago

@Zakir Husain, any other names you can think of?

- 6 months, 1 week ago

Update: For those who want to help me, click the link above and start from

$3^{193} - 2$

- 6 months, 1 week ago

Have a look at OEIS - you had better call it A014232.

- 6 months, 1 week ago

Thanks.

- 6 months, 1 week ago

I have found a further prime in the list.

- 6 months, 1 week ago

You might want to look at A014224 as well. It seems that $n=193$ is not on that list...

- 6 months, 1 week ago

Can somebody check whether this is a prime:

$121451298068529844233553416568714964256622520646270917226600348303197298080156462274524325121 = 3^{193} - 2$

- 6 months, 1 week ago

I'd love to help, but I seem to have less free time than that of the past. If you want, you can check using this calculator of factorization, if it has no factors other than itself, it is prime :)

- 6 months, 1 week ago

- 6 months, 1 week ago

\begin{aligned} 3^{193} - 2 & = \; 1214512980685298442335534165687149642566225206462709172266003483031972 98080156462274524325121 \\ & = \; 436999744065129499999522339 \times 277920753313825750274886555245065259531344474683466016812212480139 \end{aligned} is not prime. It took the Integer Factorisation Calculator two hours to find the factor, and confirm there are no others.

- 6 months, 1 week ago

- 6 months, 1 week ago

I don't know but I found a weird Pattern in the powers of 3 for which it is prime, I am still checking if the pattern holds true, and then maybe I can conjecture it. Did anyone else find something interesting 🤔

- 6 months, 1 week ago

Mersenne’s cousin

- 6 months, 1 week ago