What should I name this sequence?

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

\[3^n - 2\]

The sequence is

7,79,241,727,19681,31381059607,450283905890997361,36472996377170786401,8727963568067712425891397479476727340041447,4638397686588101979328150167890591454318967698007,1252367375378787534418600545330459692666121278462417, 79, 241, 727, 19681, 31381059607, 450283905890997361, 36472996377170786401, 8727963568067712425891397479476727340041447, 4638397686588101979328150167890591454318967698007, 125236737537878753441860054533045969266612127846241

so far.

The highest I have got is

319323^{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
4 months, 4 weeks ago

No vote yet
1 vote

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Comments

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Mersenne’s cousin

Jason Gomez - 4 months, 3 weeks ago

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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 🤔

Siddharth Chakravarty - 4 months, 3 weeks ago

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Can somebody check whether this is a prime:

121451298068529844233553416568714964256622520646270917226600348303197298080156462274524325121=31932121451298068529844233553416568714964256622520646270917226600348303197298080156462274524325121 = 3^{193} - 2

Yajat Shamji - 4 months, 4 weeks ago

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31932=  121451298068529844233553416568714964256622520646270917226600348303197298080156462274524325121=  436999744065129499999522339×277920753313825750274886555245065259531344474683466016812212480139 \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.

Mark Hennings - 4 months, 3 weeks ago

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Ahhhhh, I was about to post my answer.

Pi Han Goh - 4 months, 3 weeks ago

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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 :)

Frisk Dreemurr - 4 months, 4 weeks ago

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

Mark Hennings - 4 months, 4 weeks ago

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I have found a further prime in the list.

Yajat Shamji - 4 months, 4 weeks ago

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

Mark Hennings - 4 months, 4 weeks ago

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Thanks.

Yajat Shamji - 4 months, 4 weeks ago

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

319323^{193} - 2

Yajat Shamji - 4 months, 4 weeks ago

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

Yajat Shamji - 4 months, 4 weeks ago

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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.'

Yajat Shamji - 4 months, 4 weeks ago

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@Yajat Shamji Suggested name : Yajat primes ?

Zakir Husain - 4 months, 4 weeks ago

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