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Old 2021-01-07, 19:50   #23
Nov 2016

22×3×5×47 Posts

Originally Posted by robert44444uk View Post
I have given a little (I mean very little) thought to a set that is defined in terms of the following:

Set member z is the prime p which is the first instance of primes such that none of the primes q up to q(z-1) have a multiplicative order p-1 base q.

The set (I think) goes as follows - the first 21 members:


corresponding to the primes 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73...

An example:
271 is 135order2, 30order3, 27order5, 135order7, 135 order11, 18order13, 135 order17, 30 order19, 18 order23, 6 order29, 45 order 31, 135 order37, 45 order41, but 270 order 43.

The list is not on OEIS so happy for someone to put it up if they like.

I'm trying to think of a use.

If the p is a base in k.p^n+/-1, then it should be possible to define k much smaller than q(z-1) primorial, that provides a relatively prime series with integer n increasing, as all members of the series cannot have factors smaller than q(z-1). The efficient k values are found by applying CRM.

This is a bit akin to the Payam series, y.M(x)*2^n+/-1 with M(x) the multiple of primes that are p-1 order2, but in this new instance M(x)=1 given that all the primes to q(z-1) are considered as part of the CRM.

It might be interesting to find a few efficient k and find some primes with the bases 271 and 11971

Comments/ observations/ continuation/ efficient k/ subsequent primes welcome
The sequence (when duplicated term removed) should be A029932, your sequence is wrong.

the right sequence is 3, 7, 23, 41, 109, 191, 191, 191, 271, 271, 271, 271, 271, 271, 2791, 2791, 11971, 11971, 11971, 11971, 11971, 11971, 31771, 31771, 31771, 31771, 31771, 190321, 190321

271 and 11971 are really in the sequence, but your sequence is wrong.
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Old 2021-01-07, 20:17   #24
Batalov's Avatar
Mar 2008

24·11·53 Posts

Could you please stop necroposting?
This is your last warning.
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Old 2021-01-08, 03:31   #25
carpetpool's Avatar
Nov 2016

2×163 Posts

Déjà vu?
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Old 2021-01-08, 05:11   #26
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LaurV's Avatar
Jun 2011

52×7×53 Posts

Sweety is not a bot, we had "human" PM exchanges.

But his posts should not be in math forum, he should be restricted to his blog, or banned.
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Old 2021-01-08, 07:08   #27
Happy5214's Avatar
Nov 2008
The Alamo City

7×71 Posts

Originally Posted by LaurV View Post
But his posts should not be in math forum, he should be restricted to his blog, or banned.
Do what we do with COVID patients: mask (with a one-user usergroup) and quarantine (to his blog). Sorry, couldn't resist.
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