[seqfan] Re: Pseudo-arithmetic progressions
Vladimir Shevelev
shevelev at bgu.ac.il
Wed Jul 14 21:34:44 CEST 2010
A sense of A179382(n) is: Number of distinct odd residues contained in set {1,2,...,2^(2*n-2)} modulo 2*n-1. Thus 2*n-1 is in A001122 iff A179382(n)=n-1.
Regards,
Vladimir
----- Original Message -----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
Date: Wednesday, July 14, 2010 17:30
Subject: [seqfan] Re: Pseudo-arithmetic progressions
To: seqfan at seqfan.eu
>
> 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]
>
>
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>
Shevelev Vladimir
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