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<DIV>Joseph and Seqfans,</DIV>
<DIV> It appears that the ROUNDed values of
the sequence you describe is in the OEIS, </DIV>
<DIV>but unexpectedly as: </DIV>
<DIV>A086377: a(1)=1; a(n)=a(n-1)+2 if n is in the sequence; a(n)=a(n-1)+2 if n
and (n-1) are not in the sequence; a(n)=a(n-1)+3 if n is not in the sequence but
(n-1) is in the sequence.</DIV>
<DIV> </DIV>
<DIV>
<DIV>BUT, THERE IS AN ERROR in A086377 at position 26 and 27:</DIV>
<DIV>instead of A086377(26)=6 and A086377(27)=2, it should be joined
together as A086377(26)=62.</DIV>
<DIV> </DIV></DIV>
<DIV>So, given Joseph Bibers definition of b(n): </DIV>
<DIV>b[n] = (n-1)^2/(b[n-1] - 2*n + 3) with b[1] = 4/Pi,</DIV>
<DIV>then </DIV>
<DIV>round( b(n) ) = A086377(n).</DIV>
<DIV> </DIV>
<DIV>Does this equivalence continue to hold? If so, why?</DIV>
<DIV> Paul</DIV>
<DIV> </DIV>
<DIV>> Solving the above recurrence in the other direction we would have
<BR>> a[n] = <BR>> (n-1)^2/(a[n-1 - 2*n + 3) with a[1] =
4/Pi.<BR>> <BR>> Now consider this last defined sequence a[n]. We
suspect it grows <BR>> linearly, (1) does it? (2) What is the limit of
a[n]/n as <BR>> n->Infinity? <BR>> If this limit exists,
(3) is it in the OEIS and (4) can it be <BR>> expressed in closed form?
We suspect the value of a[1] is largely <BR>> inconsequential, (5) is
it? If this limit exists, (6) how if at all <BR>> <BR>> does it
relate to Pi?<BR></DIV></BODY></HTML>