A081853 Consider recurrence b(0) = (2n+1)/2, b(n) = b(n-1)*ceiling(b(n-1)); sequence gives first integer reached.

3, 60, 14, 268065, 33, 2093, 60, 1204154941925628, 95, 13398, 138, 701600900, 189, 47415, 248, 1489788110004539889867929328515560588293, 315, 123728, 390, 34427225343, 473, 268065, 564, 19873182780430314444725, 663, 512298, 770, 467193780498, 885, 894443, 1008

Offset: 1

Author

N. J. A. Sloane, Apr 13 2003

Keywords

• nonn

Links

• 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. A081849, A073524, A074078.

Cf. A081854.

Programs

Mathematica

a[n_]:=Module[{b=(2n+1)/2},While[!IntegerQ[b],b*=Ceiling[b]]; b]; Array[a,31] (* Stefano Spezia, Jun 26 2024 *)

Formula

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.

Extensions

a(30)-a(31) from Stefano Spezia, Jun 26 2024