<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-2022-jp">
<META content="MSHTML 6.00.2900.2180" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face="MS UI Gothic" size=2> Neil </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> These are some prime
related sequences.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> Are they fit to
OEIS?</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> If so, I will format
them.</FONT></DIV>
<DIV><FONT face="MS UI Gothic"
size=2> </FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %S
A000001 2, 1, 2, 1, 5, 3, 8, 4, 3,
14<BR> %N A000001
[Prime(n)/(Prime(n+1)-Prime(n))]</FONT></DIV>
<DIV><FONT face="MS UI Gothic"
size=2> </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> This is reciprocal
number of a distance between adjacent primes</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> </FONT><FONT
face="MS UI Gothic" size=2>%S A000002 0, -1, 1, -1, 1, -1, -1,
2, -2, <BR> %N A000002
Prime(n)-(Prime(n+1)+Prime(n-1))/2
<BR>
OffSet 5 </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> I think that it
represents a distance of Prime(n) and linear sequence.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> I awoke that it is
-1/2*{the difference of A001223}</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> %S
A000003 0, 1, 2, 1, 2, 2, 4, 3, 2, 2, 1,
<BR> %N A000003 f(m)=(m+1)/2^r ,
a(n)={minimal k such that f^k (Prime(n))=1}
<BR>
f(f(f(f(17))))=1 , so a(17)=4 </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %S
A000004 2, 1, 3, 2, 1, 1, 3, 1, 5, 1, <BR>
%N A000004 2^a(n) is the largest power of two dividing
(Prime(n)+1) </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> It appears when we
use P+1 prime test.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> Yasutoshi</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2>
</FONT></DIV></BODY></HTML>