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A087675 Consider recurrence b(0) = (2n+1)/2, b(n) = b(0)*floor(b(n-1)); sequence gives first integer reached.

%I A087675 #19 Oct 23 2023 15:54:57
%S A087675 5,35,18,814,39,390,68,72827,105,1449,150,31887,203,3596,264,27852510,
%T A087675 333,7215,410,208464,495,12690,588,10561998,689,20405,798,744049,915,
%U A087675 30744,1040,46620858503,1173,44091,1314,1950450,1463,60830,1620,121575329,1785
%N A087675 Consider recurrence b(0) = (2n+1)/2, b(n) = b(0)*floor(b(n-1)); sequence gives first integer reached.
%H A087675 Robert Israel, <a href="/A087675/b087675.txt">Table of n, a(n) for n = 2..10000</a>
%H A087675 J. C. Lagarias and N. J. A. Sloane, Approximate squaring (<a href="http://neilsloane.com/doc/apsq.pdf">pdf</a>, <a href="http://neilsloane.com/doc/apsq.ps">ps</a>), Experimental Math., 13 (2004), 113-128.
%F A087675 The even-indexed terms are given by A007742.
%p A087675 f:= proc(n)
%p A087675   local b0, b;
%p A087675   b0:= (2*n+1)/2;
%p A087675   b:= b0;
%p A087675   do
%p A087675     b:= b0*floor(b);
%p A087675     if b::integer then return b fi
%p A087675   od
%p A087675 end proc:
%p A087675 map(f, [$2..100]); # _Robert Israel_, Nov 25 2019
%t A087675 f[n_] := Module[{b0, b}, b0 = (2n+1)/2; b = b0; While[True, b = b0*Floor[b]; If[IntegerQ[b], Return[b]]]];
%t A087675 Table[f[n], {n, 2, 100}] (* _Jean-François Alcover_, Oct 23 2023, after _Robert Israel_ *)
%Y A087675 A001511 gives number of steps to reach an integer.
%Y A087675 Cf. A001511, A081853, A085071, A057016.
%K A087675 nonn,look
%O A087675 2,1
%A A087675 _N. J. A. Sloane_, following a suggestion of Bela Bajnok (bbajnok(AT)gettysburg.edu), Sep 27 2003
%E A087675 Offset corrected by _Robert Israel_, Nov 25 2019