[seqfan] Re: A generalized Gilbreath's conjecture, or "lizard's effect" for primes

[Vladimir Shevelev]

I am grateful to Graeme McRae (Palmdale, CA, USA) which corrected a(9) and sent me a few new terms:

1, 2, 2, 9, 7, 14, 10, 17, 21, 27, 32, 43, 35, 32, 43, 48, 50, 54, 59

Regards,
Vladimir




----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Friday, June 1, 2012 4:10
Subject: [seqfan] A generalized Gilbreath's conjecture, or "lizard's effect" for primes
To: seqfan at list.seqfan.eu

> 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?
> 
> Regards,
> Vladimir
> 
> 
>  Shevelev Vladimir‎
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
>


 Shevelev Vladimir‎