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

Offset

1,1

Links

Table of n, a(n) for n=1..29.

J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

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.

Crossrefs

A001511 gives number of steps to reach an integer. Cf. A081849, A073524, A074078.

Cf. A081854.

Sequence in context: A201184 A046024 A184951 * A183286 A195560 A229749

Adjacent sequences: A081850 A081851 A081852 * A081854 A081855 A081856

Keyword

nonn

Author

N. J. A. Sloane, Apr 13 2003

Status

approved