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

5, 35, 18, 814, 39, 390, 68, 72827, 105, 1449, 150, 31887, 203, 3596, 264, 27852510, 333, 7215, 410, 208464, 495, 12690, 588, 10561998, 689, 20405, 798, 744049, 915, 30744, 1040, 46620858503, 1173, 44091, 1314, 1950450, 1463, 60830, 1620, 121575329, 1785

Offset: 2

Author

N. J. A. Sloane, following a suggestion of Bela Bajnok (bbajnok(AT)gettysburg.edu), Sep 27 2003

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

A001511 gives number of steps to reach an integer.

Cf. A001511, A081853, A085071, A057016.

Programs

Maple

f:= proc(n)
  local b0, b;
  b0:= (2*n+1)/2;
  b:= b0;
  do
    b:= b0*floor(b);
    if b::integer then return b fi
  od
end proc:
map(f, [$2..100]); # Robert Israel, Nov 25 2019

Mathematica

f[n_] := Module[{b0, b}, b0 = (2n+1)/2; b = b0; While[True, b = b0*Floor[b]; If[IntegerQ[b], Return[b]]]];
Table[f[n], {n, 2, 100}] (* Jean-François Alcover, Oct 23 2023, after Robert Israel *)

Formula

The even-indexed terms are given by A007742.

Extensions

Offset corrected by Robert Israel, Nov 25 2019