# [seqfan] Re: Help needed!

Jack Brennen jfb at brennen.net
Wed Nov 19 22:41:51 CET 2008

```This seems to be the same sequence as those primes p > 3 such
that the order of 2 modulo p is a power of 3 or twice a
power of 3.

If that's true, then I can confirm the list is complete
up to 379081, and that the next terms after that are:

472393
1220347
1299079
5419387
6049243
28934011

Artur wrote:
> Dear Seqfans,
> Who can check that between
> 97687 and 379081 are another terms in following sequence
>
> %S A152008
> 7,19,73,163,487,1459,2593,17497,39367,52489,71119,80191,87211,97687,
> %T A152008 135433,139483,209953,262657,379081
> %N A152008 Primes which are divisors numbers of the form
> (2^EulerPhi[3^k]-1)/3^k
> %C A152008 All primes in this sequence:
> %C A152008 with exception of 7 are congruent to 1 mod 18
> %C A152008 with exception of 7, 19, 73 are congruent to 1 mod 54
> %C A152008
> %t A152008 a = {}; Do[k = ((2^EulerPhi[3^(w + 1)] - 1)/3^(w +
> 1))/((2^EulerPhi[3^w] - 1)/3^w); Do[If[Mod[k, Prime[n]] == 0,
> AppendTo[a, Prime[n]]; Print[Prime[n]]], {n, PrimePi,
> PrimePi}], {w, 1, 20}]; Union[a] (*Artur Jasinski*)
> %Y A152008 A008776, A152007
> %K A152008 hard,nice,nonn
> %O A152008 1,1
> %A A152008 Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008
>
>
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>
>

```