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

Vladimir Shevelev shevelev at bgu.ac.il
Thu May 31 22:21:42 CEST 2012

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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