[seqfan] Re: A generalized Gilbreath's conjecture, or lizard's effect for primes
g_m at mcraefamily.com
g_m at mcraefamily.com
Fri Jun 1 16:17:49 CEST 2012
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 knownÂ 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
Â appears after a time,Â Â "lizard's effect" for primes.
Â 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 Â 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 Vladimirâ€Ž
_______________________________________________
Seqfan Mailing list - http://list.seqfan.eu/
--------------------------------------------------------------------
mail2web.com – Enhanced email for the mobile individual based on Microsoft®
Exchange - http://link.mail2web.com/Personal/EnhancedEmail
More information about the SeqFan
mailing list