[seqfan] Re: A generalized Gilbreath's conjecture, or "lizard's effect" for primes
njasloane at gmail.com
Fri Jun 1 16:38:34 CEST 2012
Re generalizations of Gilbreath's conjecture: see references in A036262,
especially the Odlyzko paper.
On Thu, May 31, 2012 at 4:21 PM, Vladimir Shevelev <shevelev at bgu.ac.il>wrote:
> Dear SeqFans,
> A very known Gilbreath's conjecture states that the k-th iteration (k>=1)
> of the absolute values of differences of consecutive primes always begins
> from 1. I believe that, if to consider 2 followed by the consecutive primes
> beginning with the n-th prime p_n, n>=2, then there exists an iteration
> which begins from 1 and, moreover, after the first such iteration all other
> iterations begin with 1. I call this effect, when the "tail" of 1's
> appears after a time, "lizard's effect" for primes.
> Denote by a(n) (n>=2) the number of the first iteration beginning from 1.
> Then I obtained by handy a(2)=1, a(3)=2 (for primes 2,5,7,11,...), a(4)=2
> (for primes 2,7,11,13,...), a(5)=9, a(6)=7, a(7)=14, a(8)=10, a(9)=11.
> What is the continuation of this sequence?
> Shevelev Vladimir
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