A068857 a(0) = 0, a(1) = 8; for n>=2: a(n) = smallest multiple of a(n-1) which is of the form 2k*(2k+2).

0, 8, 24, 48, 288, 16128, 11950848, 4636929024, 88106288385024, 8038489644431643930624, 15177535939786079616000991061008232448, 40096515501441989312471498490435884509054125751527350190658560000

Offset: 0

Author

Amarnath Murthy, Mar 12 2002

Keywords

• nonn

Examples

			24 = 4*6 is a member and the smallest multiple of 24 which is of the form 2k(2k+2) is 48 = 6*8.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..14

Crossrefs

Cf. A000217, A033996, A068776.

Programs

Mathematica

m = 0; {0} ~Join~ Rest@ NestList[(m++; While[! Divisible[Set[k, # (# + 2) &[2 m]], #], m++]; k) &, 1, 8] (* Michael De Vlieger, Mar 18 2024 *)

Python

from itertools import islice
from sympy import sqrt_mod_iter
def A068857_gen(): # generator of terms
    yield 0
    a = 8
    while True:
        yield a
        b = a+1
        for d in sqrt_mod_iter(1,a):
            if d==1 or d**2-1 == a:
                d += a
            if d&1 and d < b:
                b = d
        a = b**2-1
A068857_list = list(islice(A068857_gen(),11)) # Chai Wah Wu, May 05 2024

Formula

a(n) = 8 * A068776(n-1) for n>=1.

Extensions

More terms from Sascha Kurz, Mar 23 2002

a(8) onward corrected by Sean A. Irvine, Mar 18 2024

a(10)-a(11) from Alois P. Heinz, Mar 19 2024