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<DIV><FONT face="MS UI Gothic" size=2> Neil</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> Sorry for the
delay.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> My condition was
not so good.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> Have I written
you a mail that I am in a rehabilitation of a sickness of
mind?</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>
<DIV> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %I
A000001<BR> %S A000001 2, 1, 2,
1, 5, 3, 8, 4, 3, 14, 5, 9<BR> %N A000001
[Prime(n)/(Prime(n+1)-Prime(n))] , where [x] means the integer part of
x.<BR> %O A000001 1, 1<BR> %K
A000001 nonn<BR> %A
A000001 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)
</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %I
A000002<BR> %S A000002 0, 1, 1, 1, 1, 1, 1,
2, 2, <BR> %V A000002 0, -1, 1, -1, 1,
-1, -1, 2, -2, <BR> %N A000002
Prime(n)-(Prime(n+1)+Prime(n-1))/2 <BR> %C
A000002 a(n)=-1/2*(A001223(n+1)-A001223(n))
<BR> %O A000002 5,
8
<BR> %K A000002 sign<BR>
%A A000002 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)
</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %I
A000003<BR> %S A000003 0, 1, 2, 1, 2, 2, 4,
3, 2, 2, 1, <BR> %N A000003
a(n)={minimal k such that f^k (Prime(n))=1}
<BR>
where f(m)=(m+1)/2^r , 2^r is the highest power of two dividing
m+1.<BR> %e A000003 f(f(f(f(17))))=1 , Prime(7)=17, so a(7)=4
<BR> %O A000003 1,
3
<BR> %K A000003 nonn<BR>
%A A000003 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)
</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %I
A000004<BR> %S A000004 0, 2, 1, 3, 2, 1, 1,
2, 3, 1, 5, 1, <BR> %N A000004 2^a(n) is the
largest power of two dividing (Prime(n)+1)
<BR> %O A000004 1,
2
<BR> %K A000003 nonn<BR>
%A A000003 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)
<BR>
<BR> %I A000005<BR> %S
A000005 1, 7, 4, 31, 31, 28, 50, 127, 91, 217, 122,
124<BR> %N A000005 Sum {|d|^2 , d|n} .
<BR>
where |d| means norm of d. d|n means d divides
n.<BR>
If norms of two divisors of n are same, then they are counted as the same
number.<BR> %e A000005 a(2)=1+|1+i|^2+2^2=7
,
<BR>
a(5)=1+|1+2i|^2+5^2=31, |1+2i|=|2+i| so they are counted as one divisor.
<BR> %O A000005 1, 2<BR> %K
A000005 nonn<BR> %A
A000005 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> This is the first line
of an array a(n,k) : Sum{|d|^2 , d|(n+k*i)} , k=0 <BR>
Do you need the sequences for k=1, 2, 3, 4 ...?<BR>
</FONT></DIV></BODY></HTML>