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

[g_m at mcraefamily.com]

Vladimir,

I get the following values for your sequence.  Thanks for suggesting it. 
You should submit it!

a(2..9)    =            1   2   2   9   7  14  10  17
a(10..19)  =   21  27  32  43  35  32  43  48  50  54
a(20..29)  =   59  78  71  69  48  75  74 100  80  85
a(30..39)  =   77 115 105 110 102 137 139 147 148 159
a(40..49)  =  156 186 151 144 156 166 167 148 222 233
a(50..59)  =  209 247 214 219 249 245 226 241 234 267
a(60..69)  =  243 233 256 292 290 269 283 351 297 321
a(70..79)  =  346 344 324 352 380 376 378 349 376 385
a(80..89)  =  422 370 398 414 416 405 417 419 466 437
a(90..99)  =  443 492 451 489 463 495 450 458 526 531
a(100..109)=  524 551 494 569 504 514 592 608 591 607

--Graeme McRae
Palmdale, CA

Original Message:
-----------------
From: Vladimir Shevelev shevelev at bgu.ac.il
Date: Thu, 31 May 2012 20:21:42 GMT
To: seqfan at list.seqfan.eu
Subject: [seqfan] A generalized Gilbreath's conjecture,or "lizard's effect"
for primes


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

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