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<DIV><FONT size=1>if b[n_] :=
Numerator[BernoulliB[2n]/(2n(2n+1))] </FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>For[n=1, n <= 1400, n++, <BR>If[ a[n] != b[n], Print[n, "
", a[n]/b[n]] ]<BR>]<BR><BR>produces </FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV>x(1) =610 y(1)= 37</DIV>
<DIV>x(2) =1276 y(2)=37</DIV>
<DIV>x(3) =1287 y(3)=103</DIV>
<DIV>x(4) =1327 y(4)=59</DIV>
<DIV> </DIV>
<DIV>and if <FONT size=1>b[n_] :=
Numerator[BernoulliB[2n]/(2n(2n-1))] </FONT></DIV>
<DIV><FONT size=1>produces</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>z(1)=547
w(1)=37</FONT></DIV>
<DIV><FONT size=1>z(2)=1185 w(2)=103</FONT></DIV>
<DIV><FONT size=1>z(3)=1240 w(3)=37</FONT></DIV>
<DIV><FONT size=1>z(4)= 1269 w(4)=59</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>I remarque that</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>z(1)/w(1) + x(1)/y(1) = 32 (integer)</FONT></DIV>
<DIV><FONT size=1>z(2)/w(2) + x(2)/y(2) = 45.9913409</FONT></DIV>
<DIV><FONT size=1>z(3)/w(3) + x(3)/y(3) = 46,0086591 </FONT></DIV>
<DIV><FONT size=1>z(4)/w(4) + x(4)/y(4) = 44 (integer)</FONT></DIV>
<DIV><FONT size=1>z(5)/w(5) + x(5)/y(5) = 22 (integer)</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>I remarque that z(2)/w(2) + x(2)/y(2)
+ z(3)/w(3) + x(3)/y(3) = 45.9913409 + 46,0086591 = 92</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>I define sequence x(n) and y(n) and the sequence z(n)/w(n) +
x(n)/y(n) if integer and another sequence z(n)/w(n) + x(n)/y(n) is not
integer</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>can anyone extend the sequence </FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>b[n_] :=
Numerator[BernoulliB[2n]/(2n(2n+1))] </FONT></DIV>
<DIV><FONT size=1>a[n_] :=
Numerator[BernoulliB[2n]/(2n)]
</FONT></DIV>
<DIV><FONT size=1></FONT> </DIV>
<DIV><FONT size=1>For[n=1, n <= ?????????, n++, <BR>If[ a[n] != b[n],
Print[n, " ", a[n]/b[n]] ]<BR>]<BR></FONT></DIV>
<DIV><FONT size=1>Thank for your help</FONT></DIV>
<DIV> </DIV>
<DIV>Merci beaucoup de votre aide<BR><BR>>>> "N. J. A. Sloane"
<njas@research.att.com> 02/03 7:56 >>><BR><BR>Dear
SeqFans, Michael Somos made an interesting discovery.<BR>A001067 and
A046968 are not the same!<BR>In fact: (speaking baby Mathematica talk, which
is<BR>all that i know): <BR><BR>a[n_] :=
Numerator[BernoulliB[2n]/(2n)]
(* A001067 *)<BR>b[n_] := Numerator[BernoulliB[2n]/(2n(2n-1))]
(* A046968 *)<BR><BR>For[n=1, n <= 580, n++, <BR>If[ a[n] != b[n], Print[n, "
", a[n]/b[n]] ]<BR>]<BR><BR>produces one line of
output<BR><BR>
574 37<BR><BR>In other words, the sequence of values of n such
that<BR>A001067(n) differs from A046968(n) starts<BR>574, ...<BR>and the
associated ratios begin<BR>37, ...<BR><BR>Could someone with more computing
power than I have extend<BR>these two sequences? PARI gives the same
result. Maple dies.<BR><BR><BR>Thanks<BR><BR>Neil<BR><BR><BR>Neil J. A.
Sloane<BR>AT&T Shannon Labs, Room C233, <BR>180 Park Avenue, Florham Park,
NJ 07932-0971<BR>Email: njas@research.att.com<BR>Office: 973 360 8415; fax: 973
360 8178<BR>Home page: <A
href="http://www.research.att.com/~njas/">http://www.research.att.com/~njas/</A><BR></DIV></BODY></HTML>