This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081853 #10 Jun 26 2024 12:21:35
%S A081853 3,60,14,268065,33,2093,60,1204154941925628,95,13398,138,701600900,
%T A081853 189,47415,248,1489788110004539889867929328515560588293,315,123728,
%U A081853 390,34427225343,473,268065,564,19873182780430314444725,663,512298,770,467193780498,885,894443,1008
%N A081853 Consider recurrence b(0) = (2n+1)/2, b(n) = b(n-1)*ceiling(b(n-1)); sequence gives first integer reached.
%H A081853 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 A081853 Define F(x) = x(x+1)/2. Write 2n+1 = 2^i*m + 2^(i-1) + 1, then a(n) = (1/2)F^(i-1)(2n+1). E.g. n=4, 2n+1 = 9 = 2^4*0 + 2^3 + 1, so i=4, m=0 and F(F(F(9))) = F(F(45)) = F(1035) = 536130, a(4) = 536130/2 = 268065.
%t A081853 a[n_]:=Module[{b=(2n+1)/2},While[!IntegerQ[b],b*=Ceiling[b]]; b]; Array[a,31] (* _Stefano Spezia_, Jun 26 2024 *)
%Y A081853 A001511 gives number of steps to reach an integer. Cf. A081849, A073524, A074078.
%Y A081853 Cf. A081854.
%K A081853 nonn
%O A081853 1,1
%A A081853 _N. J. A. Sloane_, Apr 13 2003
%E A081853 a(30)-a(31) from _Stefano Spezia_, Jun 26 2024