# [seqfan] Re: Pseudo-arithmetic progressions

Richard Mathar mathar at strw.leidenuniv.nl
Wed Jul 14 16:21:49 CEST 2010

```The conjectures in http://list.seqfan.eu/pipermail/seqfan/2010-July/005284.html are:

vs> Some very plausible conjectures for A179383:
vs>
vs>  1) The sequence consists of primes and squares of primes;
vs>  2) The set of squares is finite;
vs>  3) A prime p>=5 is in the sequence iff it has primitive root 2 (A001122);
vs>  4) For n>=2, a(n)=A139099(n+1).

Conjectures 3 and 4 are incompatible, because A139099 contains
the non-primes 1, 9=3^2, 25=5^2, 121=11^2, 1369=37^2, and no further non-prime
up to 100000. So *a**lot* of the A001122 are missing supposing A179383 and A139099
are essentially the same.

Comment submitted:
%S A139099 1,3,5,9,11,13,19,25,29,37,53,59,61,67,83,101,107,121,131,139,149,163,
%T A139099 173,179,181,197,211,227,269,293,317,347,349,373,379,389,419,421,443,
%U A139099 461,467,491,509,523,541,547,557,563,587,613,619,653,659,661,677,701
%E A139099 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 14 2010
%C A139099 Nonprimes in the sequence are 1, 9, 25, 121, 1369,... (no more up to at least 100000) [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 14 2010]

```